research article the research on low carbon logistics...
TRANSCRIPT
Research ArticleThe Research on Low Carbon Logistics Routing OptimizationBased on DNA-Ant Colony Algorithm
Liyi Zhang1 Ying Wang2 Teng Fei1 and Hongwei Ren3
1 Information Engineering College Tianjin University of Commerce Tianjin 300134 China2 Economic College Tianjin University of Commerce Tianjin 300134 China3Waston Engineering Shool State University of New York at Binghamton 138 Conklin Avenue Binghamton NY 13902 USA
Correspondence should be addressed to Teng Fei fei 8825163com
Received 11 April 2014 Accepted 15 May 2014 Published 22 June 2014
Academic Editor Xiang Li
Copyright copy 2014 Liyi Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
As the energy conservation and emission reduction and sustainable development have become the hot topics in the world lowcarbon issues catch more and more attention Logistics which is one of the important economic activities plays a crucial role inthe low carbon development Logistics leads to some significant issues about consuming energy and carbon emissions Thereforereducing energy consumption and carbon emissions has become the inevitable trend for logistics industry Low carbon logisticsis introduced in these situations In this paper from the microcosmic aspects we will bring the low carbon idea in the pathoptimization issues and change the amount of carbon emissions into carbon emissions cost to establish the path optimizationmodel based on the optimization objectives of the lowest cost of carbon emissions According to different levels of air pollutionwe will establish the double objectives path optimization model with the consideration of carbon emissions cost and economy costUse DNA-ant colony algorithm to optimize and simulate themodelThe simulation indicates that DNA-ant colony algorithm couldfind a more reasonable solution for low carbon logistics path optimization problems
1 Introduction
As the energy conservation and emission reduction and sus-tainable development has become the hot topics in theworld low carbon issues catch more and more attentionLogistics which is one important economic activity playsa crucial role in the low carbon development Logisticsleads to some significant issues about consuming energy andcarbon emissions Therefore reducing energy consumptionand carbon emissions have become the inevitable trend forlogistics industry Low carbon logistics is introduced in thesesituations Low carbon logistics means that the processesof logistics based on the goals of low energy consumptionlow pollution and low emissions use the technology ofenergy efficiency renewable energy and reducing greenhousegas emissions to restrain the harm to environment whichwould be also helpful for the purification of the logisticsenvironment and get the full use of logistics resources Itincludes logistics operation part and the whole process of
low carbon logistics management [1] Logistics operationlinks include logistics system works optimization such asreasonable planning distribution path improving logisticsefficiency reducing resources waste and taking full use oflogistics resources Logistics management includes using allkinds of low carbon technologies to improve logistics systemwhich will reduce the carbon emissions in the processes oftransportation
Low carbon logistics is one frontier domain of researchwhich catches more andmore attention of scholars Most lowcarbon logistics researches are focused on the macroscopicaspects which are the qualitative researches of low carbonlogistics including low carbon logistics itself analysis [2ndash5]low carbon logistics system analysis [6ndash8] and low carbonlogistics network analysis [9ndash11] However there are only fewresearches about microscopic aspects of low carbon logistics
In this paper from the microcosmic aspects we bring thelow carbon idea in the path optimization issues and changethe amount of carbon emissions into carbon emissions cost to
Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2014 Article ID 893851 13 pageshttpdxdoiorg1011552014893851
2 Discrete Dynamics in Nature and Society
establish the path optimizationmodel based on the optimiza-tion objectives of lowest cost of carbon emissions Accordingto different levels of air pollution we establish the doubleobjectives path optimizationmodel with the consideration ofcarbon emissions cost and economy cost We will use DNA-ant colony algorithm to optimize and simulate themodelThesimulation indicates that DNA-ant colony algorithm couldfind a more reasonable solution for low carbon logistics pathoptimization problems
2 Modeling
21 DistributionOptimizationModel ofMinimumCost of Car-bon Emissions Low carbon logistics is a kind of low energycost and low pollution logistics whose goal is to achievethe highest efficiency of logistics with the lowest greenhousegas emissions [12] Relevant data shows that thermal poweremission vehicle exhaust emissions and construction arethe main sources of carbon dioxide emissions Bearing thesocial goods transportation storage packaging processingdistribution loading unloading and other services logisticshas become the big one for the carbon emissions Looking forthe reasonable distribution route to reduce carbon emissionsis particularly important The reduction in carbon emissionsmodel reflects the reduction of carbon emissions costThere-fore this paper established low carbon logistics distributionroute optimization model to achieve the minimizing carbonemissions
211 The Calculation of Cost of Carbon Emissions As thevehicles pickup or delivery goods in the different order cross-ing all customers the car load changes With the increaseof vehicle load the unit distance fuel consumption risesleading to the increase of carbon emissions cost [13] Withthe increase of vehicle transport distance carbon emissionscost will also increaseThus the cost of carbon emissions doesnot only has relationship with transport distance but is alsorelated to the vehiclesrsquo load
The unit distance fuel consumption 120576(119902) has a linearrelationship with the total weight of the vehicles 119902sum whichis
120576 (119902) = 120575119902sum + 119887 = 120575 (119902 + 1199020) + 119887 (1)
where 120576(119902) is the unit distance fuel consumption 120575 is therelationship factor between the unit distance fuel consump-tion and vehiclesrsquo weight and 119902sum is the total weight ofthe vehicles including vehicle loading weight 119902 and vehiclersquosweight 119902
0
When vehicles are full the unit distance fuel consumptionis 120576lowast which is
120576lowast= 120575 (119876 + 119902
0) + 119887 (2)
where 120576lowast is the unit distance fuel consumption when vehiclesare full and 119876 is the vehiclesrsquo maximum load
When vehicles are empty the unit distance fuel consump-tion is 120576
0 which is
1205760= 1205751199020+ 119887 (3)
From formula (2) and formula (3) we can get
120575 =
120576lowastminus 120576 0
119876
(4)
Bring formula (4) into formula (1) the unit distance fuelconsumption 120576(119902) is as follows
120576 (119902) = 120575119902sum + 119887 = 120575 (119902 + 1199020) + 119887
= 120575119902 + (1205751199020+119887) =
120576lowastminus 1205760
119876
119902 + 1205760
(5)
Thus the carbon emissions cost CO2(119902119894119895) of the goods
with the weight 119902119894from customer 119894 to customer 119895 is as follows
CO2(119902119894119895) = 11988831205780120576 (119902119894) 119889119894119895= 11988831205780(
120576lowastminus 1205760
119876
119902119894+ 1205760)119889119894119895 (6)
where 1198883is the unit carbon emissions cost 120578
0is the carbon
emissions factor 119889119894119895
is the distance from customer 119894 tocustomer 119895 and 120578
0120576(119902119894) is the carbon emissions of the goods
with the weight 119902119894from customer 119894 to customer 119895
212 The Calculation of Cost of Carbon Emissions For theconvenience of model establishment assume that there isonly one distribution center whose location is known Allthe vehicles start from the distribution center and return todistribution center after deliveryThe vehiclesrsquo load is knownThe location and the demand of customer are known Onevehicle is for one customer
According to the above assumption establish the mini-mizing carbon emissions cost model
min CO2=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
CO2(119902119894119895) 119909119894119895119896
=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780120576 (119902119894) 119889119894119895119909119894119895119896
=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780(
120576lowastminus 1205760
119876
119902119894+ 1205760)119889119894119895119909119894119895119896
=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
119888312057801205760119889119894119895119909119894119895119896
+
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780
120576lowastminus 1205760
119876
119902119894119889119894119895119909119894119895119896
(7)
where 119871 is the number of customers 1198981015840 is the number ofvehicles 119902
119894is the demandof the 119894 customer119876 is themaximum
load of the vehicles and 119896 is the vehiclersquos number
Discrete Dynamics in Nature and Society 3
The number of distribution center is 0 The numbers ofcustomers are 1 2 3 sdot sdot sdot 119871 Define variables 119909
119894119895119896and 119910
119896119894as
119909119894119895119896=
1 vehicle 119896 from 119894 to 1198950 others
(8)
119910119896119894=
1 119894 is sevice by vehicle 1198960 others
(9)
119871
sum
119894=0
119902119894119910119896119894le 119876 119896 isin [1119898
1015840] (10)
1198981015840
sum
119896=1
119910119896119894= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (11)
119871
sum
119894=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119895 isin [0 119871] 119896 isin [1119898
1015840] (12)
119871
sum
119895=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (13)
119871
sum
119894=0
1198981015840
sum
119896=1
1199090119894119896=
119871
sum
119895=0
1198981015840
sum
119896=1
1199091198950119896 (14)
Formula (7) is the objective function The first part isthe carbon emissions cost caused by the vehiclersquos weightThe second part is the carbon emissions cost caused bythe vehiclersquos load Formula (10) shows that the sum ofcustomersrsquo demand cannot be greater than the maximumload of vehicles Formulas (11) (12) and (13) show that onevehicle is for one customer Formula (14) shows that vehiclesstart from distribution center and then return to distributioncenter
22 Double Target Distribution Optimization Model withthe Consideration of Carbon Emissions Since the increasingpollution problems the government considers the logisticsnetwork planning from the aspect of the whole area lowcarbon development to minimize the carbon emissions ofthe whole area But transportation enterprises will choosethe logistics lines based on the logistics network systemaccording to their target and determine the allocation oneach line To achieve the goal of the government and thetransport enterprises win-win this paper establishes thedouble target distribution optimization model based on ldquopayattention to carbon emissions and also give consideration toeconomyrdquoThe basic thought of amultiobjective optimizationproblem is to transfer multiobject into a numerical targetevaluation function which generally uses the linear weightedsum method [14]
Firstly the goods are delivered to the distribution centerThen the goods are sent to each customer by throughhighways waterways air transport and a variety of otherways In the whole distribution process the situation is com-plicated in which there exists not only the transformationof multiple transportation modes but also multiple layers of
distribution network In a variety of transportation modeshighway transportation is the largest one of carbon dioxideemissionsThus for the convenience of model establishmentonly consider one level of distribution network which is fromdistribution center to customer delivery and only considerthe highway transportation mode
For the convenience of model establishment make thefollowing assumptions
(1) Only consider the distribution center whose locationis known All the vehicles start from the distributioncenter After the delivery mission all the vehiclescome back to the distribution center waiting forunified deployment
(2) The delivery goods can be mixed Each customerrsquosgoods will not exceed the maximum load of thevehicle
(3) The location and demand of customers are knownOne vehicle is for one customer
(4) Load is known
(5) The vehicle serves for each affected point service andon the way only discharges without loading
According to the above assumptions establish the objectiveevaluation function
min119882 = (11988211198822) = 12058811198821+ 12058821198822 (15)
1198821=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
CO2(119902119894119895) 119909119894119895119896=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780120576 (119902119894) 119889119894119895119909119894119895119896
(16)
1198822= 11988801198981015840+
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
1198881119889119894119895119909119894119895119896
+ 1198882
1198981015840
sum
119896=1
(max119871
sum
119894=1
(119902119894119910119896119894minus 119876) 0)
(17)
119871
sum
119894=0
119902119894119910119896119894le 119876 119896 isin [1119898
1015840] (18)
1198981015840
sum
119896=1
119910119896119894= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (19)
119871
sum
119894=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119895 isin [0 119871] 119896 isin [1119898
1015840] (20)
119871
sum
119895=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (21)
4 Discrete Dynamics in Nature and Society
119871
sum
119894=0
119909119894119895119896= 119910119896119895 119894 isin [0 119871] 119896 isin [1119898
1015840] (22)
119871
sum
119895=0
119909119894119895119896= 119910119896119894 119894 isin [0 119871] 119896 isin [1119898
1015840] (23)
119871
sum
119894=0
1198981015840
sum
119896=1
1199090119894119896=
119871
sum
119895=0
1198981015840
sum
119896=1
1199091198950119896 (24)
where 1205881 1205882are the weight coefficients of the objective
function 1198880is unit vehicle cost 119888
1is unit cost of travelling
distance and 1198882is the overload punishment coefficient
Formula (15) is the objective function The lower value theobjective evaluation function has the better the path isFormula (16) is the evaluation function of carbon emissionsFormula (17) is the economic evaluation function includingthree parts The first part is the vehicle fixed cost The secondpart is the vehiclersquos transportation cost The third part isthe overload punishment cost Formulas (18) to (24) are theconstraint conditions Formula (22) shows that themission ofthe demand point 119895 is accomplished by the vehicle 119896 throughpoint 119894 Formula (23) shows that the mission of the demandpoint 119894 is accomplished by the vehicle 119896 through point 119895 Theother constraint conditions are the same as the minimumcarbon emissions cost distribution optimization model
According to the degree of pollution the air pollutionindex is divided into five levels top grade good light pol-lution moderate pollution and high level of pollution Toplevel and good level include normal activities Light pollutionincludes long-term exposure to this level air vulnerablegroupsrsquo symptoms will be slightly worse and healthy peoplewill have irritation symptoms Moderate pollution includescontacting with the air after a certain period of time symp-toms of the people with heart disease and pulmonary diseasesignificantly will increase exercise tolerance decreases andcommon symptoms happen in healthy people In high levelof pollution healthy exercise tolerance is reduced and it hasobvious symptoms and diseases According to different levelof air pollution index the values of weight coefficients ofevaluation function 120588
1 1205882are also different When the air
pollution degree is good ignore the influence of the carbonemissions cost which is 120588
1= 0 120588
2= 1 When the air
pollution is light pollution first consider the economic thenconsider carbon emissions which is 120588
1le 1205882 When the air
pollution is moderately severe pollution put the emissionreduction and energy saving in the first place with carbonemissions as the first goal and economic target as the balancewhich is 120588
1gt 1205882
3 Methods
31 Basic Ant Colony Algorithm Scientists who study socialinsect behavior characteristic found that the insect at thecommunity level of cooperation is basically self-organizingThis kind of collective behavior produced by the socialorganism which is a kind of swarm intelligence catchesthe eyes of many researchers in the fields of managementscience and engineering Ant colony algorithm is a typical
example of the use of swarm intelligence to solve combi-natorial optimization problems Ant colony algorithm as anew bionic evolutionary algorithm is published by Dorigoand Gambardella [15] The algorithm imitates ants foragingbehavior according to the heuristic idea which is causedby entrainment of pheromones gradually converging to theglobal optimal solution of the problem So far the ant colonyalgorithm has been used to solve traveling salesman problemquadratic assignment problem vehicle routing problemdynamic vehicle scheduling problem and network routingoptimization problem
Ant colony algorithm is a kind of parallel algorithmThe searching process is not starting from a point but fromthe multiple points simultaneously The distributed parallelmodel greatly improves the whole operation efficiency andquick reaction capability of the algorithm which not onlyincreases the reliability of the algorithm but also makes thealgorithm have a stronger global searching ability Ant colonyalgorithm has positive feedback characteristics which canstrengthen the optimal solution of pheromones to speed upthe convergence speed of the algorithmAnt colony algorithmhas robustness whose result is not dependent on the initialroute choice and does not need manual adjustment in theprocess Ant colony algorithm is easily combined with otherheuristic algorithms to improve the algorithm performanceAlthough the ant colony algorithm has many advantagesthere are still some defects such as long searching time slowconvergence speed slow evolution stagnation happeningeasily and precocious phenomena
Assume that there are 119899 cities The distance between anytwo cities 119894 and 119895 is 119889
119894119895(119894 119895 = 1 2 119899) 119887
119894(119905) is the number
of ants at time 119905 at city 119894119898 = sum119899119894=1119887119894(119905) is the total number of
ants 120591119894119895(119905) is the pheromone at time 119905 on the line 119894119895 At time
119905 = 0 every path has the same pheromone strength Δ120591119894119895(119905) =
0With time passing by the new pheromone is added and
old pheromones evaporate 120588 is the pheromone volatilizationcoefficient which indicates pheromones volatile speedWhenall the ants accomplish one travel pheromone on every pathis
120591119894119895 (119905 + 1) = (1 minus 120588) 120591119894119895 (
119905) + Δ120591119894119895 (119905) (25)
Δ120591119894119895(119905) =
119898
sum
119896=1
Δ120591119896
119894119895(119905) (26)
where Δ120591119894119895(119905) is the pheromone increment on the path 119894119895
At the beginning Δ120591119894119895(0) = 0 Δ120591119896
119894119895(119905) is the pheromone
released by ant 119896 on the path 119894119895 which is determined bythe ants performance The more the paths are the more thepheromone is
Δ119896
119894119895(119905) =
119876
119871119896
section 119896 of ants pass edge
119894119895 in the course of this tour0 else
(27)
Discrete Dynamics in Nature and Society 5
where119876 is constant and 119871119896is the path length of the ant 119896The
transition probability of ant 119896 from city 119894 to city 119895 is
119875119896
119894119895=
[120591119894119895 (119905)]
120572
sdot [120578119894119895 (119905)]
120573
sum119904isinallowed119896 [120591119894119904 (119905)]
120572sdot [120578119894119904(119905)]120573
119895 isin allowed119896
0 others
(28)
where allowed119896= (1 2 119899) minus tabu
119896indicates that the city
collection ant 119896 can choose currently tabu119896(119896 = 1 2 119898)
is the taboo table of ant 119896 which indicates the cities ant 119896has passed by to show the memory of ants 120578
119894119895(119905) is prior
knowledge visibility In the TSP problem it is the heuristicinformation from one city moved to another city which isgenerally 120578
119894119895(119905) = 1119889
119894119895 120572 is the importance of the residual
information on the path 119894119895120573 is the importance of the heuristicinformation
The basic ant colony algorithm to achieve the process isthat 119898 ants start from one certain city at the same time tochoose the next city based on Formula (28) which indicatesthat ants prefer visiting the path with higher intensity ofpheromone The passed cities will be put into tabu
119896 After
all ants finish one travel renew the pheromone on each pathbased on Formula (25) to Formula (27) Repeat the aboveprocesses until termination condition is established
32 DNA-Ant Colony Algorithm Solution Model The numer-ous studies of ant colony algorithm have shown its signif-icance in the optimization combination problem but thereare still some shortcomings such as seeking to local optimalsolution rather than the global optimal solution and conver-gence lag In particular for the selection of basic ant colonyalgorithm parameters there is no theoretical derivation butrelying on the results of experiments The selection of antcolony algorithm parameters is directly related to the effec-tiveness of the algorithmrsquos solution If the parameter selectionis improper it will seriously affect the performance of theant colony algorithmDNA-ant colony algorithm controls theparameter selection by the crossover and mutation idea ofDNA algorithm to optimize the performance of ant colonyalgorithm which will overcome the shortcomings of antcolony algorithm to improve the convergence rate and searchthe global optimal solution
DNA the so-called deoxyribonucleic acid is the mostimportant biological macromolecules of organisms in thenature and the main genetic materials for all creaturesThe discovery of DNA double helix structure marks thedevelopment of biological science which has entered thephase of molecular biology DNA is a kind of high molecularcompound which is the basic unit of DNA nucleotides Eachdeoxyribonucleotide is composed of a molecular phosphatemolecular DNA nucleotides and a molecule nitrogenousbase Nitrogenous base includes adenine deoxynucleotide(A) guanine oligodeoxynucleotides (G) cytosine deoxyri-bonucleotide (C) and thymidine nucleotide (T) Modernmolecular biology believes that DNA is the main materialbasis of biological inheritance which stored the geneticinformation It transfers genetic information from parentto offspring by self-copy transfer and generates the RNA
transcription (ribonucleic acid) to translate into specificproteins to control the phenomenon of life [16ndash18] DNAmolecule with the double helix structure is circled by thetwo parallel deoxynucleotides long chain Deoxyribose andphosphate in DNA molecule alternately link and arrangeon the outer side constituting the basic skeleton The baseson the two chains are linked together by hydrogen bondsforming base pairs Base pairs follow the principle of com-plementary base pairing namely purines and pyrimidinesmatching that is adenine (A) and thymine (T) must bematched and guanine (G) and cytosine (C) must be matchedAlthough deoxyribose and phosphate arrange stably on thedeoxyribonucleotide long chains the order of base pairs isprotean on the long chain There are only four bases andtwo methods of four types of the four bases to form theDNA molecules but different orders of base pairs constitutea wealth of information [19]
The crossover andmutation inDNAalgorithm is differentfrom genetic algorithm Crossover and mutation in DNAalgorithm is based on gene level with a different encodingmethod which is two digits binary encoding instead of unitbinary encoding The crossover operation of DNA algorithmis based on the two-point crossover method with a certainprobability 119901
119888 which means that a part of bases swaps
randomly in the deoxyribonucleotide long chains to formnew deoxyribonucleotide long chains (see Figure 11)
Transform coding method of DNA algorithm into twobinary coding method can be recognized by computerswhich is A-00 T-01 C-10 G-11 and 00 with 01 and 10 with11 (see Figure 12)
Mutation of DNA algorithm is based on purine replacingpurine and pyrimidine replacing pyrimidine with A chang-ing into G and C changing into T Bases correspond to binarymachines coding method with 00 changing with 11 and10 changing with 01 In the mutation the base sequencesmutation operates in a certain probability 119901
119898(see Figure 13)
DNA-ant colony algorithm optimizes the parameters120572 120573 120588 of the basic ant colony algorithm based on thecrossover and mutation ideas of DNA algorithm to solvethe low carbon logistics route optimization problems Thesolution processes of low carbon logistics route optimizationbased on DNA-ant colony algorithm is as shown in Figure 1The pseudocode of low carbon logistics route optimizationbased on DNA-Ant colony algorithm is as follows
(1) The basic ant colony algorithm parameters initializa-tion is as follows
119873119862 = 0 (119873119862 is the number of iterations)119871119900119886119889 = 0 (119871119900119886119889 is the vehicle load)120591119894119895(0) = 0 (the pheromone on branch 119894119895 is 0)
(2) The DNA ant colony algorithm parameters initializa-tion is as follows
119863119873119860 119873119880119872 = 10 (119863119873119860 119873119880119872 is the numberof updating generation of DNA algorithm)120572(1119873119880119872) (119886 is importancematrix of the resid-ual information)
6 Discrete Dynamics in Nature and Society
yes
No
N
Y
YEnd
N
Initialization ant colony algorithm parameters
Initialization DNA-ant colony algorithmparameters
m ants are on the distribution center
Tabu is full
Calculation of the target function
Cross and mutate
Update the pheromone
Select the optimum NUM2 as parent DNA
Start
Calculation of transition probability select and move on to the next city j and add j to tabu
clear tabu NC = NCmax
NC = NC + 1
Overloaded
Figure 1 The model solution flow chart of DNA-ant colony algorithm
120573(1119873119880119872) (120573 is the importance matrix of theinspiring pheromone)
120588(1119873119880119872) (120588 is the matrix of pheromone vola-tilization coefficient)
119901119888= 06 (119901
119888is the crossover probability of DNA
algorithm)
119901119898= 008 (119901
119898is the mutation probability of
DNA algorithm)
Discrete Dynamics in Nature and Society 7
(3) Operate crossover and mutation of DNA algorithmare as follows
for 1 to119863119873119860 119873119880119872 dorepeat Steps (3)sim(8)operate crossover and mutation of DNA algo-rithmfor 1 to119873119880119872 dorepeat Steps (4)sim(7)
(4) Put 119898 ants at the distribution center The number ofdistribution center 1 in the array tabu to form the arraytabu(1) is as follows
while119873119862 lt 119873119862maxfor 119894 = 1 to119898 do119869 = 1 23 119899 minus tabu(1) (119869 is the matrix of thecities will be visited)
(5) 119896 = 119896 + 1
calculate the transition probability of antsaccording to Formula (28)119871119900119886119889 = 119871119900119886119889 + 119871119900119886119889 119904119890119903V119890119903(119896)if 119871119900119886119889 le 119871119900119886119889 maxant 119894 goes to the next City 119895 Choose and moveto the next City 119895 and put 119895 into array tabuelseant 119894 returns to distribution center and putdistribution center with number 1 into arraytabu119871119900119886119889 = 0repeat Step (5) until all the cities have travelledthrough and then check whether tabu is full Ifnot return to Step (5) Otherwise go on to Step(6)
(6) for 119894 = 1 to119898 do
calculate the path length 119897 to solve the objectivefunction (the values of minimum carbon emis-sions cost function or the objective evaluationfunction) and record the current best solutionUpdate the pheromone based on the formula(25)
(7) if119873119862 lt 119873119862max
119873119862 = 119873119862 + 1 (29)
and then clean up tabu and return to Step (4)
(8) Choose the better 1198731198801198722 as the parent DNA tooperate the crossover and mutation Get the new120572 120573 120588 parameter matrices and return to Step (3)
4 Results and Discussion
Assume the distribution center has 16 customers whosecoordinate is (00) Table 1 is the demand of each customerTable 2 is the coordinate of each customer The maximumload of each vehicle is 75 tons In the simulation set 119888
0=
0 1198881= 1 119888
2= infin The unit distance fuel cost of empty car
and full car is 1205760= 1 and 120576lowast = 2 The unit carbon emissions
cost is 1198883= 03 The emission factor is 120578 = 261 [20] The
distances between each customer and distribution center canbe calculated by Formula (30)
119889119894119895= radic(119909
119894minus 119909119895)
2
+ (119910119894minus 119910119895)
2
(30)
Table 3 shows the 10 results by using the basic ant colonyalgorithm to solve the minimum carbon emissions costmodel Table 4 shows the 10 results by using the DNA-antcolony algorithm to solve the minimum carbon emissionscost model Comparing Table 3 with Table 4 we can find thefollowing
(1) Carbon emissions cost the minimum carbon emis-sions cost of basic ant colony algorithm is 4265and the cost of DNA-ant colony algorithm is 3988The DNA-ant colony algorithm saves 64 of min-imum carbon emissions cost compared with basicant colony algorithm The average carbon emissionscost of basic ant colony algorithm is 5462 Theaverage cost of DNA-Ant colony algorithm is 47034For the average carbon emissions cost the DNA-antcolony algorithm saves 138 comparedwith basic antcolony algorithmThus for the solution of minimumcarbon emissions cost distribution model DNA-antcolony algorithm can find the path with less carbonemissions cost which is better for environmentalprotection
(2) The number of final generation the average numberof final generation of basic ant colony algorithm is1337The average number of final generation of DNA-ant colony algorithm is 81 From the average numberof final generation we can find that the DNA-antcolony algorithm has a better convergence
(3) The difference with minimum carbon emissions costthe average difference between basic ant colonyalgorithm and minimum carbon emissions cost is1197The average difference betweenDNA-ant colonyalgorithm and minimum carbon emissions cost is7154 From the difference with minimum carbonemissions cost we can find that the DNA-Ant colonyalgorithm is more stable in the process of searchminimum carbon emissions
Figure 2 is the distribution path of basic ant colony based ontheminimumcarbon emissions costmodelTheprocesses areas follows
Distribution CenterrarrCustomer13rarrCustomer10rarrCustomer11rarrDistribution Center
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
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2 Discrete Dynamics in Nature and Society
establish the path optimizationmodel based on the optimiza-tion objectives of lowest cost of carbon emissions Accordingto different levels of air pollution we establish the doubleobjectives path optimizationmodel with the consideration ofcarbon emissions cost and economy cost We will use DNA-ant colony algorithm to optimize and simulate themodelThesimulation indicates that DNA-ant colony algorithm couldfind a more reasonable solution for low carbon logistics pathoptimization problems
2 Modeling
21 DistributionOptimizationModel ofMinimumCost of Car-bon Emissions Low carbon logistics is a kind of low energycost and low pollution logistics whose goal is to achievethe highest efficiency of logistics with the lowest greenhousegas emissions [12] Relevant data shows that thermal poweremission vehicle exhaust emissions and construction arethe main sources of carbon dioxide emissions Bearing thesocial goods transportation storage packaging processingdistribution loading unloading and other services logisticshas become the big one for the carbon emissions Looking forthe reasonable distribution route to reduce carbon emissionsis particularly important The reduction in carbon emissionsmodel reflects the reduction of carbon emissions costThere-fore this paper established low carbon logistics distributionroute optimization model to achieve the minimizing carbonemissions
211 The Calculation of Cost of Carbon Emissions As thevehicles pickup or delivery goods in the different order cross-ing all customers the car load changes With the increaseof vehicle load the unit distance fuel consumption risesleading to the increase of carbon emissions cost [13] Withthe increase of vehicle transport distance carbon emissionscost will also increaseThus the cost of carbon emissions doesnot only has relationship with transport distance but is alsorelated to the vehiclesrsquo load
The unit distance fuel consumption 120576(119902) has a linearrelationship with the total weight of the vehicles 119902sum whichis
120576 (119902) = 120575119902sum + 119887 = 120575 (119902 + 1199020) + 119887 (1)
where 120576(119902) is the unit distance fuel consumption 120575 is therelationship factor between the unit distance fuel consump-tion and vehiclesrsquo weight and 119902sum is the total weight ofthe vehicles including vehicle loading weight 119902 and vehiclersquosweight 119902
0
When vehicles are full the unit distance fuel consumptionis 120576lowast which is
120576lowast= 120575 (119876 + 119902
0) + 119887 (2)
where 120576lowast is the unit distance fuel consumption when vehiclesare full and 119876 is the vehiclesrsquo maximum load
When vehicles are empty the unit distance fuel consump-tion is 120576
0 which is
1205760= 1205751199020+ 119887 (3)
From formula (2) and formula (3) we can get
120575 =
120576lowastminus 120576 0
119876
(4)
Bring formula (4) into formula (1) the unit distance fuelconsumption 120576(119902) is as follows
120576 (119902) = 120575119902sum + 119887 = 120575 (119902 + 1199020) + 119887
= 120575119902 + (1205751199020+119887) =
120576lowastminus 1205760
119876
119902 + 1205760
(5)
Thus the carbon emissions cost CO2(119902119894119895) of the goods
with the weight 119902119894from customer 119894 to customer 119895 is as follows
CO2(119902119894119895) = 11988831205780120576 (119902119894) 119889119894119895= 11988831205780(
120576lowastminus 1205760
119876
119902119894+ 1205760)119889119894119895 (6)
where 1198883is the unit carbon emissions cost 120578
0is the carbon
emissions factor 119889119894119895
is the distance from customer 119894 tocustomer 119895 and 120578
0120576(119902119894) is the carbon emissions of the goods
with the weight 119902119894from customer 119894 to customer 119895
212 The Calculation of Cost of Carbon Emissions For theconvenience of model establishment assume that there isonly one distribution center whose location is known Allthe vehicles start from the distribution center and return todistribution center after deliveryThe vehiclesrsquo load is knownThe location and the demand of customer are known Onevehicle is for one customer
According to the above assumption establish the mini-mizing carbon emissions cost model
min CO2=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
CO2(119902119894119895) 119909119894119895119896
=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780120576 (119902119894) 119889119894119895119909119894119895119896
=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780(
120576lowastminus 1205760
119876
119902119894+ 1205760)119889119894119895119909119894119895119896
=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
119888312057801205760119889119894119895119909119894119895119896
+
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780
120576lowastminus 1205760
119876
119902119894119889119894119895119909119894119895119896
(7)
where 119871 is the number of customers 1198981015840 is the number ofvehicles 119902
119894is the demandof the 119894 customer119876 is themaximum
load of the vehicles and 119896 is the vehiclersquos number
Discrete Dynamics in Nature and Society 3
The number of distribution center is 0 The numbers ofcustomers are 1 2 3 sdot sdot sdot 119871 Define variables 119909
119894119895119896and 119910
119896119894as
119909119894119895119896=
1 vehicle 119896 from 119894 to 1198950 others
(8)
119910119896119894=
1 119894 is sevice by vehicle 1198960 others
(9)
119871
sum
119894=0
119902119894119910119896119894le 119876 119896 isin [1119898
1015840] (10)
1198981015840
sum
119896=1
119910119896119894= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (11)
119871
sum
119894=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119895 isin [0 119871] 119896 isin [1119898
1015840] (12)
119871
sum
119895=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (13)
119871
sum
119894=0
1198981015840
sum
119896=1
1199090119894119896=
119871
sum
119895=0
1198981015840
sum
119896=1
1199091198950119896 (14)
Formula (7) is the objective function The first part isthe carbon emissions cost caused by the vehiclersquos weightThe second part is the carbon emissions cost caused bythe vehiclersquos load Formula (10) shows that the sum ofcustomersrsquo demand cannot be greater than the maximumload of vehicles Formulas (11) (12) and (13) show that onevehicle is for one customer Formula (14) shows that vehiclesstart from distribution center and then return to distributioncenter
22 Double Target Distribution Optimization Model withthe Consideration of Carbon Emissions Since the increasingpollution problems the government considers the logisticsnetwork planning from the aspect of the whole area lowcarbon development to minimize the carbon emissions ofthe whole area But transportation enterprises will choosethe logistics lines based on the logistics network systemaccording to their target and determine the allocation oneach line To achieve the goal of the government and thetransport enterprises win-win this paper establishes thedouble target distribution optimization model based on ldquopayattention to carbon emissions and also give consideration toeconomyrdquoThe basic thought of amultiobjective optimizationproblem is to transfer multiobject into a numerical targetevaluation function which generally uses the linear weightedsum method [14]
Firstly the goods are delivered to the distribution centerThen the goods are sent to each customer by throughhighways waterways air transport and a variety of otherways In the whole distribution process the situation is com-plicated in which there exists not only the transformationof multiple transportation modes but also multiple layers of
distribution network In a variety of transportation modeshighway transportation is the largest one of carbon dioxideemissionsThus for the convenience of model establishmentonly consider one level of distribution network which is fromdistribution center to customer delivery and only considerthe highway transportation mode
For the convenience of model establishment make thefollowing assumptions
(1) Only consider the distribution center whose locationis known All the vehicles start from the distributioncenter After the delivery mission all the vehiclescome back to the distribution center waiting forunified deployment
(2) The delivery goods can be mixed Each customerrsquosgoods will not exceed the maximum load of thevehicle
(3) The location and demand of customers are knownOne vehicle is for one customer
(4) Load is known
(5) The vehicle serves for each affected point service andon the way only discharges without loading
According to the above assumptions establish the objectiveevaluation function
min119882 = (11988211198822) = 12058811198821+ 12058821198822 (15)
1198821=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
CO2(119902119894119895) 119909119894119895119896=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780120576 (119902119894) 119889119894119895119909119894119895119896
(16)
1198822= 11988801198981015840+
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
1198881119889119894119895119909119894119895119896
+ 1198882
1198981015840
sum
119896=1
(max119871
sum
119894=1
(119902119894119910119896119894minus 119876) 0)
(17)
119871
sum
119894=0
119902119894119910119896119894le 119876 119896 isin [1119898
1015840] (18)
1198981015840
sum
119896=1
119910119896119894= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (19)
119871
sum
119894=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119895 isin [0 119871] 119896 isin [1119898
1015840] (20)
119871
sum
119895=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (21)
4 Discrete Dynamics in Nature and Society
119871
sum
119894=0
119909119894119895119896= 119910119896119895 119894 isin [0 119871] 119896 isin [1119898
1015840] (22)
119871
sum
119895=0
119909119894119895119896= 119910119896119894 119894 isin [0 119871] 119896 isin [1119898
1015840] (23)
119871
sum
119894=0
1198981015840
sum
119896=1
1199090119894119896=
119871
sum
119895=0
1198981015840
sum
119896=1
1199091198950119896 (24)
where 1205881 1205882are the weight coefficients of the objective
function 1198880is unit vehicle cost 119888
1is unit cost of travelling
distance and 1198882is the overload punishment coefficient
Formula (15) is the objective function The lower value theobjective evaluation function has the better the path isFormula (16) is the evaluation function of carbon emissionsFormula (17) is the economic evaluation function includingthree parts The first part is the vehicle fixed cost The secondpart is the vehiclersquos transportation cost The third part isthe overload punishment cost Formulas (18) to (24) are theconstraint conditions Formula (22) shows that themission ofthe demand point 119895 is accomplished by the vehicle 119896 throughpoint 119894 Formula (23) shows that the mission of the demandpoint 119894 is accomplished by the vehicle 119896 through point 119895 Theother constraint conditions are the same as the minimumcarbon emissions cost distribution optimization model
According to the degree of pollution the air pollutionindex is divided into five levels top grade good light pol-lution moderate pollution and high level of pollution Toplevel and good level include normal activities Light pollutionincludes long-term exposure to this level air vulnerablegroupsrsquo symptoms will be slightly worse and healthy peoplewill have irritation symptoms Moderate pollution includescontacting with the air after a certain period of time symp-toms of the people with heart disease and pulmonary diseasesignificantly will increase exercise tolerance decreases andcommon symptoms happen in healthy people In high levelof pollution healthy exercise tolerance is reduced and it hasobvious symptoms and diseases According to different levelof air pollution index the values of weight coefficients ofevaluation function 120588
1 1205882are also different When the air
pollution degree is good ignore the influence of the carbonemissions cost which is 120588
1= 0 120588
2= 1 When the air
pollution is light pollution first consider the economic thenconsider carbon emissions which is 120588
1le 1205882 When the air
pollution is moderately severe pollution put the emissionreduction and energy saving in the first place with carbonemissions as the first goal and economic target as the balancewhich is 120588
1gt 1205882
3 Methods
31 Basic Ant Colony Algorithm Scientists who study socialinsect behavior characteristic found that the insect at thecommunity level of cooperation is basically self-organizingThis kind of collective behavior produced by the socialorganism which is a kind of swarm intelligence catchesthe eyes of many researchers in the fields of managementscience and engineering Ant colony algorithm is a typical
example of the use of swarm intelligence to solve combi-natorial optimization problems Ant colony algorithm as anew bionic evolutionary algorithm is published by Dorigoand Gambardella [15] The algorithm imitates ants foragingbehavior according to the heuristic idea which is causedby entrainment of pheromones gradually converging to theglobal optimal solution of the problem So far the ant colonyalgorithm has been used to solve traveling salesman problemquadratic assignment problem vehicle routing problemdynamic vehicle scheduling problem and network routingoptimization problem
Ant colony algorithm is a kind of parallel algorithmThe searching process is not starting from a point but fromthe multiple points simultaneously The distributed parallelmodel greatly improves the whole operation efficiency andquick reaction capability of the algorithm which not onlyincreases the reliability of the algorithm but also makes thealgorithm have a stronger global searching ability Ant colonyalgorithm has positive feedback characteristics which canstrengthen the optimal solution of pheromones to speed upthe convergence speed of the algorithmAnt colony algorithmhas robustness whose result is not dependent on the initialroute choice and does not need manual adjustment in theprocess Ant colony algorithm is easily combined with otherheuristic algorithms to improve the algorithm performanceAlthough the ant colony algorithm has many advantagesthere are still some defects such as long searching time slowconvergence speed slow evolution stagnation happeningeasily and precocious phenomena
Assume that there are 119899 cities The distance between anytwo cities 119894 and 119895 is 119889
119894119895(119894 119895 = 1 2 119899) 119887
119894(119905) is the number
of ants at time 119905 at city 119894119898 = sum119899119894=1119887119894(119905) is the total number of
ants 120591119894119895(119905) is the pheromone at time 119905 on the line 119894119895 At time
119905 = 0 every path has the same pheromone strength Δ120591119894119895(119905) =
0With time passing by the new pheromone is added and
old pheromones evaporate 120588 is the pheromone volatilizationcoefficient which indicates pheromones volatile speedWhenall the ants accomplish one travel pheromone on every pathis
120591119894119895 (119905 + 1) = (1 minus 120588) 120591119894119895 (
119905) + Δ120591119894119895 (119905) (25)
Δ120591119894119895(119905) =
119898
sum
119896=1
Δ120591119896
119894119895(119905) (26)
where Δ120591119894119895(119905) is the pheromone increment on the path 119894119895
At the beginning Δ120591119894119895(0) = 0 Δ120591119896
119894119895(119905) is the pheromone
released by ant 119896 on the path 119894119895 which is determined bythe ants performance The more the paths are the more thepheromone is
Δ119896
119894119895(119905) =
119876
119871119896
section 119896 of ants pass edge
119894119895 in the course of this tour0 else
(27)
Discrete Dynamics in Nature and Society 5
where119876 is constant and 119871119896is the path length of the ant 119896The
transition probability of ant 119896 from city 119894 to city 119895 is
119875119896
119894119895=
[120591119894119895 (119905)]
120572
sdot [120578119894119895 (119905)]
120573
sum119904isinallowed119896 [120591119894119904 (119905)]
120572sdot [120578119894119904(119905)]120573
119895 isin allowed119896
0 others
(28)
where allowed119896= (1 2 119899) minus tabu
119896indicates that the city
collection ant 119896 can choose currently tabu119896(119896 = 1 2 119898)
is the taboo table of ant 119896 which indicates the cities ant 119896has passed by to show the memory of ants 120578
119894119895(119905) is prior
knowledge visibility In the TSP problem it is the heuristicinformation from one city moved to another city which isgenerally 120578
119894119895(119905) = 1119889
119894119895 120572 is the importance of the residual
information on the path 119894119895120573 is the importance of the heuristicinformation
The basic ant colony algorithm to achieve the process isthat 119898 ants start from one certain city at the same time tochoose the next city based on Formula (28) which indicatesthat ants prefer visiting the path with higher intensity ofpheromone The passed cities will be put into tabu
119896 After
all ants finish one travel renew the pheromone on each pathbased on Formula (25) to Formula (27) Repeat the aboveprocesses until termination condition is established
32 DNA-Ant Colony Algorithm Solution Model The numer-ous studies of ant colony algorithm have shown its signif-icance in the optimization combination problem but thereare still some shortcomings such as seeking to local optimalsolution rather than the global optimal solution and conver-gence lag In particular for the selection of basic ant colonyalgorithm parameters there is no theoretical derivation butrelying on the results of experiments The selection of antcolony algorithm parameters is directly related to the effec-tiveness of the algorithmrsquos solution If the parameter selectionis improper it will seriously affect the performance of theant colony algorithmDNA-ant colony algorithm controls theparameter selection by the crossover and mutation idea ofDNA algorithm to optimize the performance of ant colonyalgorithm which will overcome the shortcomings of antcolony algorithm to improve the convergence rate and searchthe global optimal solution
DNA the so-called deoxyribonucleic acid is the mostimportant biological macromolecules of organisms in thenature and the main genetic materials for all creaturesThe discovery of DNA double helix structure marks thedevelopment of biological science which has entered thephase of molecular biology DNA is a kind of high molecularcompound which is the basic unit of DNA nucleotides Eachdeoxyribonucleotide is composed of a molecular phosphatemolecular DNA nucleotides and a molecule nitrogenousbase Nitrogenous base includes adenine deoxynucleotide(A) guanine oligodeoxynucleotides (G) cytosine deoxyri-bonucleotide (C) and thymidine nucleotide (T) Modernmolecular biology believes that DNA is the main materialbasis of biological inheritance which stored the geneticinformation It transfers genetic information from parentto offspring by self-copy transfer and generates the RNA
transcription (ribonucleic acid) to translate into specificproteins to control the phenomenon of life [16ndash18] DNAmolecule with the double helix structure is circled by thetwo parallel deoxynucleotides long chain Deoxyribose andphosphate in DNA molecule alternately link and arrangeon the outer side constituting the basic skeleton The baseson the two chains are linked together by hydrogen bondsforming base pairs Base pairs follow the principle of com-plementary base pairing namely purines and pyrimidinesmatching that is adenine (A) and thymine (T) must bematched and guanine (G) and cytosine (C) must be matchedAlthough deoxyribose and phosphate arrange stably on thedeoxyribonucleotide long chains the order of base pairs isprotean on the long chain There are only four bases andtwo methods of four types of the four bases to form theDNA molecules but different orders of base pairs constitutea wealth of information [19]
The crossover andmutation inDNAalgorithm is differentfrom genetic algorithm Crossover and mutation in DNAalgorithm is based on gene level with a different encodingmethod which is two digits binary encoding instead of unitbinary encoding The crossover operation of DNA algorithmis based on the two-point crossover method with a certainprobability 119901
119888 which means that a part of bases swaps
randomly in the deoxyribonucleotide long chains to formnew deoxyribonucleotide long chains (see Figure 11)
Transform coding method of DNA algorithm into twobinary coding method can be recognized by computerswhich is A-00 T-01 C-10 G-11 and 00 with 01 and 10 with11 (see Figure 12)
Mutation of DNA algorithm is based on purine replacingpurine and pyrimidine replacing pyrimidine with A chang-ing into G and C changing into T Bases correspond to binarymachines coding method with 00 changing with 11 and10 changing with 01 In the mutation the base sequencesmutation operates in a certain probability 119901
119898(see Figure 13)
DNA-ant colony algorithm optimizes the parameters120572 120573 120588 of the basic ant colony algorithm based on thecrossover and mutation ideas of DNA algorithm to solvethe low carbon logistics route optimization problems Thesolution processes of low carbon logistics route optimizationbased on DNA-ant colony algorithm is as shown in Figure 1The pseudocode of low carbon logistics route optimizationbased on DNA-Ant colony algorithm is as follows
(1) The basic ant colony algorithm parameters initializa-tion is as follows
119873119862 = 0 (119873119862 is the number of iterations)119871119900119886119889 = 0 (119871119900119886119889 is the vehicle load)120591119894119895(0) = 0 (the pheromone on branch 119894119895 is 0)
(2) The DNA ant colony algorithm parameters initializa-tion is as follows
119863119873119860 119873119880119872 = 10 (119863119873119860 119873119880119872 is the numberof updating generation of DNA algorithm)120572(1119873119880119872) (119886 is importancematrix of the resid-ual information)
6 Discrete Dynamics in Nature and Society
yes
No
N
Y
YEnd
N
Initialization ant colony algorithm parameters
Initialization DNA-ant colony algorithmparameters
m ants are on the distribution center
Tabu is full
Calculation of the target function
Cross and mutate
Update the pheromone
Select the optimum NUM2 as parent DNA
Start
Calculation of transition probability select and move on to the next city j and add j to tabu
clear tabu NC = NCmax
NC = NC + 1
Overloaded
Figure 1 The model solution flow chart of DNA-ant colony algorithm
120573(1119873119880119872) (120573 is the importance matrix of theinspiring pheromone)
120588(1119873119880119872) (120588 is the matrix of pheromone vola-tilization coefficient)
119901119888= 06 (119901
119888is the crossover probability of DNA
algorithm)
119901119898= 008 (119901
119898is the mutation probability of
DNA algorithm)
Discrete Dynamics in Nature and Society 7
(3) Operate crossover and mutation of DNA algorithmare as follows
for 1 to119863119873119860 119873119880119872 dorepeat Steps (3)sim(8)operate crossover and mutation of DNA algo-rithmfor 1 to119873119880119872 dorepeat Steps (4)sim(7)
(4) Put 119898 ants at the distribution center The number ofdistribution center 1 in the array tabu to form the arraytabu(1) is as follows
while119873119862 lt 119873119862maxfor 119894 = 1 to119898 do119869 = 1 23 119899 minus tabu(1) (119869 is the matrix of thecities will be visited)
(5) 119896 = 119896 + 1
calculate the transition probability of antsaccording to Formula (28)119871119900119886119889 = 119871119900119886119889 + 119871119900119886119889 119904119890119903V119890119903(119896)if 119871119900119886119889 le 119871119900119886119889 maxant 119894 goes to the next City 119895 Choose and moveto the next City 119895 and put 119895 into array tabuelseant 119894 returns to distribution center and putdistribution center with number 1 into arraytabu119871119900119886119889 = 0repeat Step (5) until all the cities have travelledthrough and then check whether tabu is full Ifnot return to Step (5) Otherwise go on to Step(6)
(6) for 119894 = 1 to119898 do
calculate the path length 119897 to solve the objectivefunction (the values of minimum carbon emis-sions cost function or the objective evaluationfunction) and record the current best solutionUpdate the pheromone based on the formula(25)
(7) if119873119862 lt 119873119862max
119873119862 = 119873119862 + 1 (29)
and then clean up tabu and return to Step (4)
(8) Choose the better 1198731198801198722 as the parent DNA tooperate the crossover and mutation Get the new120572 120573 120588 parameter matrices and return to Step (3)
4 Results and Discussion
Assume the distribution center has 16 customers whosecoordinate is (00) Table 1 is the demand of each customerTable 2 is the coordinate of each customer The maximumload of each vehicle is 75 tons In the simulation set 119888
0=
0 1198881= 1 119888
2= infin The unit distance fuel cost of empty car
and full car is 1205760= 1 and 120576lowast = 2 The unit carbon emissions
cost is 1198883= 03 The emission factor is 120578 = 261 [20] The
distances between each customer and distribution center canbe calculated by Formula (30)
119889119894119895= radic(119909
119894minus 119909119895)
2
+ (119910119894minus 119910119895)
2
(30)
Table 3 shows the 10 results by using the basic ant colonyalgorithm to solve the minimum carbon emissions costmodel Table 4 shows the 10 results by using the DNA-antcolony algorithm to solve the minimum carbon emissionscost model Comparing Table 3 with Table 4 we can find thefollowing
(1) Carbon emissions cost the minimum carbon emis-sions cost of basic ant colony algorithm is 4265and the cost of DNA-ant colony algorithm is 3988The DNA-ant colony algorithm saves 64 of min-imum carbon emissions cost compared with basicant colony algorithm The average carbon emissionscost of basic ant colony algorithm is 5462 Theaverage cost of DNA-Ant colony algorithm is 47034For the average carbon emissions cost the DNA-antcolony algorithm saves 138 comparedwith basic antcolony algorithmThus for the solution of minimumcarbon emissions cost distribution model DNA-antcolony algorithm can find the path with less carbonemissions cost which is better for environmentalprotection
(2) The number of final generation the average numberof final generation of basic ant colony algorithm is1337The average number of final generation of DNA-ant colony algorithm is 81 From the average numberof final generation we can find that the DNA-antcolony algorithm has a better convergence
(3) The difference with minimum carbon emissions costthe average difference between basic ant colonyalgorithm and minimum carbon emissions cost is1197The average difference betweenDNA-ant colonyalgorithm and minimum carbon emissions cost is7154 From the difference with minimum carbonemissions cost we can find that the DNA-Ant colonyalgorithm is more stable in the process of searchminimum carbon emissions
Figure 2 is the distribution path of basic ant colony based ontheminimumcarbon emissions costmodelTheprocesses areas follows
Distribution CenterrarrCustomer13rarrCustomer10rarrCustomer11rarrDistribution Center
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Discrete Dynamics in Nature and Society
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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Discrete Dynamics in Nature and Society 3
The number of distribution center is 0 The numbers ofcustomers are 1 2 3 sdot sdot sdot 119871 Define variables 119909
119894119895119896and 119910
119896119894as
119909119894119895119896=
1 vehicle 119896 from 119894 to 1198950 others
(8)
119910119896119894=
1 119894 is sevice by vehicle 1198960 others
(9)
119871
sum
119894=0
119902119894119910119896119894le 119876 119896 isin [1119898
1015840] (10)
1198981015840
sum
119896=1
119910119896119894= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (11)
119871
sum
119894=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119895 isin [0 119871] 119896 isin [1119898
1015840] (12)
119871
sum
119895=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (13)
119871
sum
119894=0
1198981015840
sum
119896=1
1199090119894119896=
119871
sum
119895=0
1198981015840
sum
119896=1
1199091198950119896 (14)
Formula (7) is the objective function The first part isthe carbon emissions cost caused by the vehiclersquos weightThe second part is the carbon emissions cost caused bythe vehiclersquos load Formula (10) shows that the sum ofcustomersrsquo demand cannot be greater than the maximumload of vehicles Formulas (11) (12) and (13) show that onevehicle is for one customer Formula (14) shows that vehiclesstart from distribution center and then return to distributioncenter
22 Double Target Distribution Optimization Model withthe Consideration of Carbon Emissions Since the increasingpollution problems the government considers the logisticsnetwork planning from the aspect of the whole area lowcarbon development to minimize the carbon emissions ofthe whole area But transportation enterprises will choosethe logistics lines based on the logistics network systemaccording to their target and determine the allocation oneach line To achieve the goal of the government and thetransport enterprises win-win this paper establishes thedouble target distribution optimization model based on ldquopayattention to carbon emissions and also give consideration toeconomyrdquoThe basic thought of amultiobjective optimizationproblem is to transfer multiobject into a numerical targetevaluation function which generally uses the linear weightedsum method [14]
Firstly the goods are delivered to the distribution centerThen the goods are sent to each customer by throughhighways waterways air transport and a variety of otherways In the whole distribution process the situation is com-plicated in which there exists not only the transformationof multiple transportation modes but also multiple layers of
distribution network In a variety of transportation modeshighway transportation is the largest one of carbon dioxideemissionsThus for the convenience of model establishmentonly consider one level of distribution network which is fromdistribution center to customer delivery and only considerthe highway transportation mode
For the convenience of model establishment make thefollowing assumptions
(1) Only consider the distribution center whose locationis known All the vehicles start from the distributioncenter After the delivery mission all the vehiclescome back to the distribution center waiting forunified deployment
(2) The delivery goods can be mixed Each customerrsquosgoods will not exceed the maximum load of thevehicle
(3) The location and demand of customers are knownOne vehicle is for one customer
(4) Load is known
(5) The vehicle serves for each affected point service andon the way only discharges without loading
According to the above assumptions establish the objectiveevaluation function
min119882 = (11988211198822) = 12058811198821+ 12058821198822 (15)
1198821=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
CO2(119902119894119895) 119909119894119895119896=
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
11988831205780120576 (119902119894) 119889119894119895119909119894119895119896
(16)
1198822= 11988801198981015840+
119871
sum
119894=0
119871
sum
119895=0
1198981015840
sum
119896=1
1198881119889119894119895119909119894119895119896
+ 1198882
1198981015840
sum
119896=1
(max119871
sum
119894=1
(119902119894119910119896119894minus 119876) 0)
(17)
119871
sum
119894=0
119902119894119910119896119894le 119876 119896 isin [1119898
1015840] (18)
1198981015840
sum
119896=1
119910119896119894= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (19)
119871
sum
119894=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119895 isin [0 119871] 119896 isin [1119898
1015840] (20)
119871
sum
119895=0
1198981015840
sum
119896=1
119909119894119895119896= 1 119894 isin [0 119871] 119896 isin [1119898
1015840] (21)
4 Discrete Dynamics in Nature and Society
119871
sum
119894=0
119909119894119895119896= 119910119896119895 119894 isin [0 119871] 119896 isin [1119898
1015840] (22)
119871
sum
119895=0
119909119894119895119896= 119910119896119894 119894 isin [0 119871] 119896 isin [1119898
1015840] (23)
119871
sum
119894=0
1198981015840
sum
119896=1
1199090119894119896=
119871
sum
119895=0
1198981015840
sum
119896=1
1199091198950119896 (24)
where 1205881 1205882are the weight coefficients of the objective
function 1198880is unit vehicle cost 119888
1is unit cost of travelling
distance and 1198882is the overload punishment coefficient
Formula (15) is the objective function The lower value theobjective evaluation function has the better the path isFormula (16) is the evaluation function of carbon emissionsFormula (17) is the economic evaluation function includingthree parts The first part is the vehicle fixed cost The secondpart is the vehiclersquos transportation cost The third part isthe overload punishment cost Formulas (18) to (24) are theconstraint conditions Formula (22) shows that themission ofthe demand point 119895 is accomplished by the vehicle 119896 throughpoint 119894 Formula (23) shows that the mission of the demandpoint 119894 is accomplished by the vehicle 119896 through point 119895 Theother constraint conditions are the same as the minimumcarbon emissions cost distribution optimization model
According to the degree of pollution the air pollutionindex is divided into five levels top grade good light pol-lution moderate pollution and high level of pollution Toplevel and good level include normal activities Light pollutionincludes long-term exposure to this level air vulnerablegroupsrsquo symptoms will be slightly worse and healthy peoplewill have irritation symptoms Moderate pollution includescontacting with the air after a certain period of time symp-toms of the people with heart disease and pulmonary diseasesignificantly will increase exercise tolerance decreases andcommon symptoms happen in healthy people In high levelof pollution healthy exercise tolerance is reduced and it hasobvious symptoms and diseases According to different levelof air pollution index the values of weight coefficients ofevaluation function 120588
1 1205882are also different When the air
pollution degree is good ignore the influence of the carbonemissions cost which is 120588
1= 0 120588
2= 1 When the air
pollution is light pollution first consider the economic thenconsider carbon emissions which is 120588
1le 1205882 When the air
pollution is moderately severe pollution put the emissionreduction and energy saving in the first place with carbonemissions as the first goal and economic target as the balancewhich is 120588
1gt 1205882
3 Methods
31 Basic Ant Colony Algorithm Scientists who study socialinsect behavior characteristic found that the insect at thecommunity level of cooperation is basically self-organizingThis kind of collective behavior produced by the socialorganism which is a kind of swarm intelligence catchesthe eyes of many researchers in the fields of managementscience and engineering Ant colony algorithm is a typical
example of the use of swarm intelligence to solve combi-natorial optimization problems Ant colony algorithm as anew bionic evolutionary algorithm is published by Dorigoand Gambardella [15] The algorithm imitates ants foragingbehavior according to the heuristic idea which is causedby entrainment of pheromones gradually converging to theglobal optimal solution of the problem So far the ant colonyalgorithm has been used to solve traveling salesman problemquadratic assignment problem vehicle routing problemdynamic vehicle scheduling problem and network routingoptimization problem
Ant colony algorithm is a kind of parallel algorithmThe searching process is not starting from a point but fromthe multiple points simultaneously The distributed parallelmodel greatly improves the whole operation efficiency andquick reaction capability of the algorithm which not onlyincreases the reliability of the algorithm but also makes thealgorithm have a stronger global searching ability Ant colonyalgorithm has positive feedback characteristics which canstrengthen the optimal solution of pheromones to speed upthe convergence speed of the algorithmAnt colony algorithmhas robustness whose result is not dependent on the initialroute choice and does not need manual adjustment in theprocess Ant colony algorithm is easily combined with otherheuristic algorithms to improve the algorithm performanceAlthough the ant colony algorithm has many advantagesthere are still some defects such as long searching time slowconvergence speed slow evolution stagnation happeningeasily and precocious phenomena
Assume that there are 119899 cities The distance between anytwo cities 119894 and 119895 is 119889
119894119895(119894 119895 = 1 2 119899) 119887
119894(119905) is the number
of ants at time 119905 at city 119894119898 = sum119899119894=1119887119894(119905) is the total number of
ants 120591119894119895(119905) is the pheromone at time 119905 on the line 119894119895 At time
119905 = 0 every path has the same pheromone strength Δ120591119894119895(119905) =
0With time passing by the new pheromone is added and
old pheromones evaporate 120588 is the pheromone volatilizationcoefficient which indicates pheromones volatile speedWhenall the ants accomplish one travel pheromone on every pathis
120591119894119895 (119905 + 1) = (1 minus 120588) 120591119894119895 (
119905) + Δ120591119894119895 (119905) (25)
Δ120591119894119895(119905) =
119898
sum
119896=1
Δ120591119896
119894119895(119905) (26)
where Δ120591119894119895(119905) is the pheromone increment on the path 119894119895
At the beginning Δ120591119894119895(0) = 0 Δ120591119896
119894119895(119905) is the pheromone
released by ant 119896 on the path 119894119895 which is determined bythe ants performance The more the paths are the more thepheromone is
Δ119896
119894119895(119905) =
119876
119871119896
section 119896 of ants pass edge
119894119895 in the course of this tour0 else
(27)
Discrete Dynamics in Nature and Society 5
where119876 is constant and 119871119896is the path length of the ant 119896The
transition probability of ant 119896 from city 119894 to city 119895 is
119875119896
119894119895=
[120591119894119895 (119905)]
120572
sdot [120578119894119895 (119905)]
120573
sum119904isinallowed119896 [120591119894119904 (119905)]
120572sdot [120578119894119904(119905)]120573
119895 isin allowed119896
0 others
(28)
where allowed119896= (1 2 119899) minus tabu
119896indicates that the city
collection ant 119896 can choose currently tabu119896(119896 = 1 2 119898)
is the taboo table of ant 119896 which indicates the cities ant 119896has passed by to show the memory of ants 120578
119894119895(119905) is prior
knowledge visibility In the TSP problem it is the heuristicinformation from one city moved to another city which isgenerally 120578
119894119895(119905) = 1119889
119894119895 120572 is the importance of the residual
information on the path 119894119895120573 is the importance of the heuristicinformation
The basic ant colony algorithm to achieve the process isthat 119898 ants start from one certain city at the same time tochoose the next city based on Formula (28) which indicatesthat ants prefer visiting the path with higher intensity ofpheromone The passed cities will be put into tabu
119896 After
all ants finish one travel renew the pheromone on each pathbased on Formula (25) to Formula (27) Repeat the aboveprocesses until termination condition is established
32 DNA-Ant Colony Algorithm Solution Model The numer-ous studies of ant colony algorithm have shown its signif-icance in the optimization combination problem but thereare still some shortcomings such as seeking to local optimalsolution rather than the global optimal solution and conver-gence lag In particular for the selection of basic ant colonyalgorithm parameters there is no theoretical derivation butrelying on the results of experiments The selection of antcolony algorithm parameters is directly related to the effec-tiveness of the algorithmrsquos solution If the parameter selectionis improper it will seriously affect the performance of theant colony algorithmDNA-ant colony algorithm controls theparameter selection by the crossover and mutation idea ofDNA algorithm to optimize the performance of ant colonyalgorithm which will overcome the shortcomings of antcolony algorithm to improve the convergence rate and searchthe global optimal solution
DNA the so-called deoxyribonucleic acid is the mostimportant biological macromolecules of organisms in thenature and the main genetic materials for all creaturesThe discovery of DNA double helix structure marks thedevelopment of biological science which has entered thephase of molecular biology DNA is a kind of high molecularcompound which is the basic unit of DNA nucleotides Eachdeoxyribonucleotide is composed of a molecular phosphatemolecular DNA nucleotides and a molecule nitrogenousbase Nitrogenous base includes adenine deoxynucleotide(A) guanine oligodeoxynucleotides (G) cytosine deoxyri-bonucleotide (C) and thymidine nucleotide (T) Modernmolecular biology believes that DNA is the main materialbasis of biological inheritance which stored the geneticinformation It transfers genetic information from parentto offspring by self-copy transfer and generates the RNA
transcription (ribonucleic acid) to translate into specificproteins to control the phenomenon of life [16ndash18] DNAmolecule with the double helix structure is circled by thetwo parallel deoxynucleotides long chain Deoxyribose andphosphate in DNA molecule alternately link and arrangeon the outer side constituting the basic skeleton The baseson the two chains are linked together by hydrogen bondsforming base pairs Base pairs follow the principle of com-plementary base pairing namely purines and pyrimidinesmatching that is adenine (A) and thymine (T) must bematched and guanine (G) and cytosine (C) must be matchedAlthough deoxyribose and phosphate arrange stably on thedeoxyribonucleotide long chains the order of base pairs isprotean on the long chain There are only four bases andtwo methods of four types of the four bases to form theDNA molecules but different orders of base pairs constitutea wealth of information [19]
The crossover andmutation inDNAalgorithm is differentfrom genetic algorithm Crossover and mutation in DNAalgorithm is based on gene level with a different encodingmethod which is two digits binary encoding instead of unitbinary encoding The crossover operation of DNA algorithmis based on the two-point crossover method with a certainprobability 119901
119888 which means that a part of bases swaps
randomly in the deoxyribonucleotide long chains to formnew deoxyribonucleotide long chains (see Figure 11)
Transform coding method of DNA algorithm into twobinary coding method can be recognized by computerswhich is A-00 T-01 C-10 G-11 and 00 with 01 and 10 with11 (see Figure 12)
Mutation of DNA algorithm is based on purine replacingpurine and pyrimidine replacing pyrimidine with A chang-ing into G and C changing into T Bases correspond to binarymachines coding method with 00 changing with 11 and10 changing with 01 In the mutation the base sequencesmutation operates in a certain probability 119901
119898(see Figure 13)
DNA-ant colony algorithm optimizes the parameters120572 120573 120588 of the basic ant colony algorithm based on thecrossover and mutation ideas of DNA algorithm to solvethe low carbon logistics route optimization problems Thesolution processes of low carbon logistics route optimizationbased on DNA-ant colony algorithm is as shown in Figure 1The pseudocode of low carbon logistics route optimizationbased on DNA-Ant colony algorithm is as follows
(1) The basic ant colony algorithm parameters initializa-tion is as follows
119873119862 = 0 (119873119862 is the number of iterations)119871119900119886119889 = 0 (119871119900119886119889 is the vehicle load)120591119894119895(0) = 0 (the pheromone on branch 119894119895 is 0)
(2) The DNA ant colony algorithm parameters initializa-tion is as follows
119863119873119860 119873119880119872 = 10 (119863119873119860 119873119880119872 is the numberof updating generation of DNA algorithm)120572(1119873119880119872) (119886 is importancematrix of the resid-ual information)
6 Discrete Dynamics in Nature and Society
yes
No
N
Y
YEnd
N
Initialization ant colony algorithm parameters
Initialization DNA-ant colony algorithmparameters
m ants are on the distribution center
Tabu is full
Calculation of the target function
Cross and mutate
Update the pheromone
Select the optimum NUM2 as parent DNA
Start
Calculation of transition probability select and move on to the next city j and add j to tabu
clear tabu NC = NCmax
NC = NC + 1
Overloaded
Figure 1 The model solution flow chart of DNA-ant colony algorithm
120573(1119873119880119872) (120573 is the importance matrix of theinspiring pheromone)
120588(1119873119880119872) (120588 is the matrix of pheromone vola-tilization coefficient)
119901119888= 06 (119901
119888is the crossover probability of DNA
algorithm)
119901119898= 008 (119901
119898is the mutation probability of
DNA algorithm)
Discrete Dynamics in Nature and Society 7
(3) Operate crossover and mutation of DNA algorithmare as follows
for 1 to119863119873119860 119873119880119872 dorepeat Steps (3)sim(8)operate crossover and mutation of DNA algo-rithmfor 1 to119873119880119872 dorepeat Steps (4)sim(7)
(4) Put 119898 ants at the distribution center The number ofdistribution center 1 in the array tabu to form the arraytabu(1) is as follows
while119873119862 lt 119873119862maxfor 119894 = 1 to119898 do119869 = 1 23 119899 minus tabu(1) (119869 is the matrix of thecities will be visited)
(5) 119896 = 119896 + 1
calculate the transition probability of antsaccording to Formula (28)119871119900119886119889 = 119871119900119886119889 + 119871119900119886119889 119904119890119903V119890119903(119896)if 119871119900119886119889 le 119871119900119886119889 maxant 119894 goes to the next City 119895 Choose and moveto the next City 119895 and put 119895 into array tabuelseant 119894 returns to distribution center and putdistribution center with number 1 into arraytabu119871119900119886119889 = 0repeat Step (5) until all the cities have travelledthrough and then check whether tabu is full Ifnot return to Step (5) Otherwise go on to Step(6)
(6) for 119894 = 1 to119898 do
calculate the path length 119897 to solve the objectivefunction (the values of minimum carbon emis-sions cost function or the objective evaluationfunction) and record the current best solutionUpdate the pheromone based on the formula(25)
(7) if119873119862 lt 119873119862max
119873119862 = 119873119862 + 1 (29)
and then clean up tabu and return to Step (4)
(8) Choose the better 1198731198801198722 as the parent DNA tooperate the crossover and mutation Get the new120572 120573 120588 parameter matrices and return to Step (3)
4 Results and Discussion
Assume the distribution center has 16 customers whosecoordinate is (00) Table 1 is the demand of each customerTable 2 is the coordinate of each customer The maximumload of each vehicle is 75 tons In the simulation set 119888
0=
0 1198881= 1 119888
2= infin The unit distance fuel cost of empty car
and full car is 1205760= 1 and 120576lowast = 2 The unit carbon emissions
cost is 1198883= 03 The emission factor is 120578 = 261 [20] The
distances between each customer and distribution center canbe calculated by Formula (30)
119889119894119895= radic(119909
119894minus 119909119895)
2
+ (119910119894minus 119910119895)
2
(30)
Table 3 shows the 10 results by using the basic ant colonyalgorithm to solve the minimum carbon emissions costmodel Table 4 shows the 10 results by using the DNA-antcolony algorithm to solve the minimum carbon emissionscost model Comparing Table 3 with Table 4 we can find thefollowing
(1) Carbon emissions cost the minimum carbon emis-sions cost of basic ant colony algorithm is 4265and the cost of DNA-ant colony algorithm is 3988The DNA-ant colony algorithm saves 64 of min-imum carbon emissions cost compared with basicant colony algorithm The average carbon emissionscost of basic ant colony algorithm is 5462 Theaverage cost of DNA-Ant colony algorithm is 47034For the average carbon emissions cost the DNA-antcolony algorithm saves 138 comparedwith basic antcolony algorithmThus for the solution of minimumcarbon emissions cost distribution model DNA-antcolony algorithm can find the path with less carbonemissions cost which is better for environmentalprotection
(2) The number of final generation the average numberof final generation of basic ant colony algorithm is1337The average number of final generation of DNA-ant colony algorithm is 81 From the average numberof final generation we can find that the DNA-antcolony algorithm has a better convergence
(3) The difference with minimum carbon emissions costthe average difference between basic ant colonyalgorithm and minimum carbon emissions cost is1197The average difference betweenDNA-ant colonyalgorithm and minimum carbon emissions cost is7154 From the difference with minimum carbonemissions cost we can find that the DNA-Ant colonyalgorithm is more stable in the process of searchminimum carbon emissions
Figure 2 is the distribution path of basic ant colony based ontheminimumcarbon emissions costmodelTheprocesses areas follows
Distribution CenterrarrCustomer13rarrCustomer10rarrCustomer11rarrDistribution Center
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
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4 Discrete Dynamics in Nature and Society
119871
sum
119894=0
119909119894119895119896= 119910119896119895 119894 isin [0 119871] 119896 isin [1119898
1015840] (22)
119871
sum
119895=0
119909119894119895119896= 119910119896119894 119894 isin [0 119871] 119896 isin [1119898
1015840] (23)
119871
sum
119894=0
1198981015840
sum
119896=1
1199090119894119896=
119871
sum
119895=0
1198981015840
sum
119896=1
1199091198950119896 (24)
where 1205881 1205882are the weight coefficients of the objective
function 1198880is unit vehicle cost 119888
1is unit cost of travelling
distance and 1198882is the overload punishment coefficient
Formula (15) is the objective function The lower value theobjective evaluation function has the better the path isFormula (16) is the evaluation function of carbon emissionsFormula (17) is the economic evaluation function includingthree parts The first part is the vehicle fixed cost The secondpart is the vehiclersquos transportation cost The third part isthe overload punishment cost Formulas (18) to (24) are theconstraint conditions Formula (22) shows that themission ofthe demand point 119895 is accomplished by the vehicle 119896 throughpoint 119894 Formula (23) shows that the mission of the demandpoint 119894 is accomplished by the vehicle 119896 through point 119895 Theother constraint conditions are the same as the minimumcarbon emissions cost distribution optimization model
According to the degree of pollution the air pollutionindex is divided into five levels top grade good light pol-lution moderate pollution and high level of pollution Toplevel and good level include normal activities Light pollutionincludes long-term exposure to this level air vulnerablegroupsrsquo symptoms will be slightly worse and healthy peoplewill have irritation symptoms Moderate pollution includescontacting with the air after a certain period of time symp-toms of the people with heart disease and pulmonary diseasesignificantly will increase exercise tolerance decreases andcommon symptoms happen in healthy people In high levelof pollution healthy exercise tolerance is reduced and it hasobvious symptoms and diseases According to different levelof air pollution index the values of weight coefficients ofevaluation function 120588
1 1205882are also different When the air
pollution degree is good ignore the influence of the carbonemissions cost which is 120588
1= 0 120588
2= 1 When the air
pollution is light pollution first consider the economic thenconsider carbon emissions which is 120588
1le 1205882 When the air
pollution is moderately severe pollution put the emissionreduction and energy saving in the first place with carbonemissions as the first goal and economic target as the balancewhich is 120588
1gt 1205882
3 Methods
31 Basic Ant Colony Algorithm Scientists who study socialinsect behavior characteristic found that the insect at thecommunity level of cooperation is basically self-organizingThis kind of collective behavior produced by the socialorganism which is a kind of swarm intelligence catchesthe eyes of many researchers in the fields of managementscience and engineering Ant colony algorithm is a typical
example of the use of swarm intelligence to solve combi-natorial optimization problems Ant colony algorithm as anew bionic evolutionary algorithm is published by Dorigoand Gambardella [15] The algorithm imitates ants foragingbehavior according to the heuristic idea which is causedby entrainment of pheromones gradually converging to theglobal optimal solution of the problem So far the ant colonyalgorithm has been used to solve traveling salesman problemquadratic assignment problem vehicle routing problemdynamic vehicle scheduling problem and network routingoptimization problem
Ant colony algorithm is a kind of parallel algorithmThe searching process is not starting from a point but fromthe multiple points simultaneously The distributed parallelmodel greatly improves the whole operation efficiency andquick reaction capability of the algorithm which not onlyincreases the reliability of the algorithm but also makes thealgorithm have a stronger global searching ability Ant colonyalgorithm has positive feedback characteristics which canstrengthen the optimal solution of pheromones to speed upthe convergence speed of the algorithmAnt colony algorithmhas robustness whose result is not dependent on the initialroute choice and does not need manual adjustment in theprocess Ant colony algorithm is easily combined with otherheuristic algorithms to improve the algorithm performanceAlthough the ant colony algorithm has many advantagesthere are still some defects such as long searching time slowconvergence speed slow evolution stagnation happeningeasily and precocious phenomena
Assume that there are 119899 cities The distance between anytwo cities 119894 and 119895 is 119889
119894119895(119894 119895 = 1 2 119899) 119887
119894(119905) is the number
of ants at time 119905 at city 119894119898 = sum119899119894=1119887119894(119905) is the total number of
ants 120591119894119895(119905) is the pheromone at time 119905 on the line 119894119895 At time
119905 = 0 every path has the same pheromone strength Δ120591119894119895(119905) =
0With time passing by the new pheromone is added and
old pheromones evaporate 120588 is the pheromone volatilizationcoefficient which indicates pheromones volatile speedWhenall the ants accomplish one travel pheromone on every pathis
120591119894119895 (119905 + 1) = (1 minus 120588) 120591119894119895 (
119905) + Δ120591119894119895 (119905) (25)
Δ120591119894119895(119905) =
119898
sum
119896=1
Δ120591119896
119894119895(119905) (26)
where Δ120591119894119895(119905) is the pheromone increment on the path 119894119895
At the beginning Δ120591119894119895(0) = 0 Δ120591119896
119894119895(119905) is the pheromone
released by ant 119896 on the path 119894119895 which is determined bythe ants performance The more the paths are the more thepheromone is
Δ119896
119894119895(119905) =
119876
119871119896
section 119896 of ants pass edge
119894119895 in the course of this tour0 else
(27)
Discrete Dynamics in Nature and Society 5
where119876 is constant and 119871119896is the path length of the ant 119896The
transition probability of ant 119896 from city 119894 to city 119895 is
119875119896
119894119895=
[120591119894119895 (119905)]
120572
sdot [120578119894119895 (119905)]
120573
sum119904isinallowed119896 [120591119894119904 (119905)]
120572sdot [120578119894119904(119905)]120573
119895 isin allowed119896
0 others
(28)
where allowed119896= (1 2 119899) minus tabu
119896indicates that the city
collection ant 119896 can choose currently tabu119896(119896 = 1 2 119898)
is the taboo table of ant 119896 which indicates the cities ant 119896has passed by to show the memory of ants 120578
119894119895(119905) is prior
knowledge visibility In the TSP problem it is the heuristicinformation from one city moved to another city which isgenerally 120578
119894119895(119905) = 1119889
119894119895 120572 is the importance of the residual
information on the path 119894119895120573 is the importance of the heuristicinformation
The basic ant colony algorithm to achieve the process isthat 119898 ants start from one certain city at the same time tochoose the next city based on Formula (28) which indicatesthat ants prefer visiting the path with higher intensity ofpheromone The passed cities will be put into tabu
119896 After
all ants finish one travel renew the pheromone on each pathbased on Formula (25) to Formula (27) Repeat the aboveprocesses until termination condition is established
32 DNA-Ant Colony Algorithm Solution Model The numer-ous studies of ant colony algorithm have shown its signif-icance in the optimization combination problem but thereare still some shortcomings such as seeking to local optimalsolution rather than the global optimal solution and conver-gence lag In particular for the selection of basic ant colonyalgorithm parameters there is no theoretical derivation butrelying on the results of experiments The selection of antcolony algorithm parameters is directly related to the effec-tiveness of the algorithmrsquos solution If the parameter selectionis improper it will seriously affect the performance of theant colony algorithmDNA-ant colony algorithm controls theparameter selection by the crossover and mutation idea ofDNA algorithm to optimize the performance of ant colonyalgorithm which will overcome the shortcomings of antcolony algorithm to improve the convergence rate and searchthe global optimal solution
DNA the so-called deoxyribonucleic acid is the mostimportant biological macromolecules of organisms in thenature and the main genetic materials for all creaturesThe discovery of DNA double helix structure marks thedevelopment of biological science which has entered thephase of molecular biology DNA is a kind of high molecularcompound which is the basic unit of DNA nucleotides Eachdeoxyribonucleotide is composed of a molecular phosphatemolecular DNA nucleotides and a molecule nitrogenousbase Nitrogenous base includes adenine deoxynucleotide(A) guanine oligodeoxynucleotides (G) cytosine deoxyri-bonucleotide (C) and thymidine nucleotide (T) Modernmolecular biology believes that DNA is the main materialbasis of biological inheritance which stored the geneticinformation It transfers genetic information from parentto offspring by self-copy transfer and generates the RNA
transcription (ribonucleic acid) to translate into specificproteins to control the phenomenon of life [16ndash18] DNAmolecule with the double helix structure is circled by thetwo parallel deoxynucleotides long chain Deoxyribose andphosphate in DNA molecule alternately link and arrangeon the outer side constituting the basic skeleton The baseson the two chains are linked together by hydrogen bondsforming base pairs Base pairs follow the principle of com-plementary base pairing namely purines and pyrimidinesmatching that is adenine (A) and thymine (T) must bematched and guanine (G) and cytosine (C) must be matchedAlthough deoxyribose and phosphate arrange stably on thedeoxyribonucleotide long chains the order of base pairs isprotean on the long chain There are only four bases andtwo methods of four types of the four bases to form theDNA molecules but different orders of base pairs constitutea wealth of information [19]
The crossover andmutation inDNAalgorithm is differentfrom genetic algorithm Crossover and mutation in DNAalgorithm is based on gene level with a different encodingmethod which is two digits binary encoding instead of unitbinary encoding The crossover operation of DNA algorithmis based on the two-point crossover method with a certainprobability 119901
119888 which means that a part of bases swaps
randomly in the deoxyribonucleotide long chains to formnew deoxyribonucleotide long chains (see Figure 11)
Transform coding method of DNA algorithm into twobinary coding method can be recognized by computerswhich is A-00 T-01 C-10 G-11 and 00 with 01 and 10 with11 (see Figure 12)
Mutation of DNA algorithm is based on purine replacingpurine and pyrimidine replacing pyrimidine with A chang-ing into G and C changing into T Bases correspond to binarymachines coding method with 00 changing with 11 and10 changing with 01 In the mutation the base sequencesmutation operates in a certain probability 119901
119898(see Figure 13)
DNA-ant colony algorithm optimizes the parameters120572 120573 120588 of the basic ant colony algorithm based on thecrossover and mutation ideas of DNA algorithm to solvethe low carbon logistics route optimization problems Thesolution processes of low carbon logistics route optimizationbased on DNA-ant colony algorithm is as shown in Figure 1The pseudocode of low carbon logistics route optimizationbased on DNA-Ant colony algorithm is as follows
(1) The basic ant colony algorithm parameters initializa-tion is as follows
119873119862 = 0 (119873119862 is the number of iterations)119871119900119886119889 = 0 (119871119900119886119889 is the vehicle load)120591119894119895(0) = 0 (the pheromone on branch 119894119895 is 0)
(2) The DNA ant colony algorithm parameters initializa-tion is as follows
119863119873119860 119873119880119872 = 10 (119863119873119860 119873119880119872 is the numberof updating generation of DNA algorithm)120572(1119873119880119872) (119886 is importancematrix of the resid-ual information)
6 Discrete Dynamics in Nature and Society
yes
No
N
Y
YEnd
N
Initialization ant colony algorithm parameters
Initialization DNA-ant colony algorithmparameters
m ants are on the distribution center
Tabu is full
Calculation of the target function
Cross and mutate
Update the pheromone
Select the optimum NUM2 as parent DNA
Start
Calculation of transition probability select and move on to the next city j and add j to tabu
clear tabu NC = NCmax
NC = NC + 1
Overloaded
Figure 1 The model solution flow chart of DNA-ant colony algorithm
120573(1119873119880119872) (120573 is the importance matrix of theinspiring pheromone)
120588(1119873119880119872) (120588 is the matrix of pheromone vola-tilization coefficient)
119901119888= 06 (119901
119888is the crossover probability of DNA
algorithm)
119901119898= 008 (119901
119898is the mutation probability of
DNA algorithm)
Discrete Dynamics in Nature and Society 7
(3) Operate crossover and mutation of DNA algorithmare as follows
for 1 to119863119873119860 119873119880119872 dorepeat Steps (3)sim(8)operate crossover and mutation of DNA algo-rithmfor 1 to119873119880119872 dorepeat Steps (4)sim(7)
(4) Put 119898 ants at the distribution center The number ofdistribution center 1 in the array tabu to form the arraytabu(1) is as follows
while119873119862 lt 119873119862maxfor 119894 = 1 to119898 do119869 = 1 23 119899 minus tabu(1) (119869 is the matrix of thecities will be visited)
(5) 119896 = 119896 + 1
calculate the transition probability of antsaccording to Formula (28)119871119900119886119889 = 119871119900119886119889 + 119871119900119886119889 119904119890119903V119890119903(119896)if 119871119900119886119889 le 119871119900119886119889 maxant 119894 goes to the next City 119895 Choose and moveto the next City 119895 and put 119895 into array tabuelseant 119894 returns to distribution center and putdistribution center with number 1 into arraytabu119871119900119886119889 = 0repeat Step (5) until all the cities have travelledthrough and then check whether tabu is full Ifnot return to Step (5) Otherwise go on to Step(6)
(6) for 119894 = 1 to119898 do
calculate the path length 119897 to solve the objectivefunction (the values of minimum carbon emis-sions cost function or the objective evaluationfunction) and record the current best solutionUpdate the pheromone based on the formula(25)
(7) if119873119862 lt 119873119862max
119873119862 = 119873119862 + 1 (29)
and then clean up tabu and return to Step (4)
(8) Choose the better 1198731198801198722 as the parent DNA tooperate the crossover and mutation Get the new120572 120573 120588 parameter matrices and return to Step (3)
4 Results and Discussion
Assume the distribution center has 16 customers whosecoordinate is (00) Table 1 is the demand of each customerTable 2 is the coordinate of each customer The maximumload of each vehicle is 75 tons In the simulation set 119888
0=
0 1198881= 1 119888
2= infin The unit distance fuel cost of empty car
and full car is 1205760= 1 and 120576lowast = 2 The unit carbon emissions
cost is 1198883= 03 The emission factor is 120578 = 261 [20] The
distances between each customer and distribution center canbe calculated by Formula (30)
119889119894119895= radic(119909
119894minus 119909119895)
2
+ (119910119894minus 119910119895)
2
(30)
Table 3 shows the 10 results by using the basic ant colonyalgorithm to solve the minimum carbon emissions costmodel Table 4 shows the 10 results by using the DNA-antcolony algorithm to solve the minimum carbon emissionscost model Comparing Table 3 with Table 4 we can find thefollowing
(1) Carbon emissions cost the minimum carbon emis-sions cost of basic ant colony algorithm is 4265and the cost of DNA-ant colony algorithm is 3988The DNA-ant colony algorithm saves 64 of min-imum carbon emissions cost compared with basicant colony algorithm The average carbon emissionscost of basic ant colony algorithm is 5462 Theaverage cost of DNA-Ant colony algorithm is 47034For the average carbon emissions cost the DNA-antcolony algorithm saves 138 comparedwith basic antcolony algorithmThus for the solution of minimumcarbon emissions cost distribution model DNA-antcolony algorithm can find the path with less carbonemissions cost which is better for environmentalprotection
(2) The number of final generation the average numberof final generation of basic ant colony algorithm is1337The average number of final generation of DNA-ant colony algorithm is 81 From the average numberof final generation we can find that the DNA-antcolony algorithm has a better convergence
(3) The difference with minimum carbon emissions costthe average difference between basic ant colonyalgorithm and minimum carbon emissions cost is1197The average difference betweenDNA-ant colonyalgorithm and minimum carbon emissions cost is7154 From the difference with minimum carbonemissions cost we can find that the DNA-Ant colonyalgorithm is more stable in the process of searchminimum carbon emissions
Figure 2 is the distribution path of basic ant colony based ontheminimumcarbon emissions costmodelTheprocesses areas follows
Distribution CenterrarrCustomer13rarrCustomer10rarrCustomer11rarrDistribution Center
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
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Discrete Dynamics in Nature and Society 5
where119876 is constant and 119871119896is the path length of the ant 119896The
transition probability of ant 119896 from city 119894 to city 119895 is
119875119896
119894119895=
[120591119894119895 (119905)]
120572
sdot [120578119894119895 (119905)]
120573
sum119904isinallowed119896 [120591119894119904 (119905)]
120572sdot [120578119894119904(119905)]120573
119895 isin allowed119896
0 others
(28)
where allowed119896= (1 2 119899) minus tabu
119896indicates that the city
collection ant 119896 can choose currently tabu119896(119896 = 1 2 119898)
is the taboo table of ant 119896 which indicates the cities ant 119896has passed by to show the memory of ants 120578
119894119895(119905) is prior
knowledge visibility In the TSP problem it is the heuristicinformation from one city moved to another city which isgenerally 120578
119894119895(119905) = 1119889
119894119895 120572 is the importance of the residual
information on the path 119894119895120573 is the importance of the heuristicinformation
The basic ant colony algorithm to achieve the process isthat 119898 ants start from one certain city at the same time tochoose the next city based on Formula (28) which indicatesthat ants prefer visiting the path with higher intensity ofpheromone The passed cities will be put into tabu
119896 After
all ants finish one travel renew the pheromone on each pathbased on Formula (25) to Formula (27) Repeat the aboveprocesses until termination condition is established
32 DNA-Ant Colony Algorithm Solution Model The numer-ous studies of ant colony algorithm have shown its signif-icance in the optimization combination problem but thereare still some shortcomings such as seeking to local optimalsolution rather than the global optimal solution and conver-gence lag In particular for the selection of basic ant colonyalgorithm parameters there is no theoretical derivation butrelying on the results of experiments The selection of antcolony algorithm parameters is directly related to the effec-tiveness of the algorithmrsquos solution If the parameter selectionis improper it will seriously affect the performance of theant colony algorithmDNA-ant colony algorithm controls theparameter selection by the crossover and mutation idea ofDNA algorithm to optimize the performance of ant colonyalgorithm which will overcome the shortcomings of antcolony algorithm to improve the convergence rate and searchthe global optimal solution
DNA the so-called deoxyribonucleic acid is the mostimportant biological macromolecules of organisms in thenature and the main genetic materials for all creaturesThe discovery of DNA double helix structure marks thedevelopment of biological science which has entered thephase of molecular biology DNA is a kind of high molecularcompound which is the basic unit of DNA nucleotides Eachdeoxyribonucleotide is composed of a molecular phosphatemolecular DNA nucleotides and a molecule nitrogenousbase Nitrogenous base includes adenine deoxynucleotide(A) guanine oligodeoxynucleotides (G) cytosine deoxyri-bonucleotide (C) and thymidine nucleotide (T) Modernmolecular biology believes that DNA is the main materialbasis of biological inheritance which stored the geneticinformation It transfers genetic information from parentto offspring by self-copy transfer and generates the RNA
transcription (ribonucleic acid) to translate into specificproteins to control the phenomenon of life [16ndash18] DNAmolecule with the double helix structure is circled by thetwo parallel deoxynucleotides long chain Deoxyribose andphosphate in DNA molecule alternately link and arrangeon the outer side constituting the basic skeleton The baseson the two chains are linked together by hydrogen bondsforming base pairs Base pairs follow the principle of com-plementary base pairing namely purines and pyrimidinesmatching that is adenine (A) and thymine (T) must bematched and guanine (G) and cytosine (C) must be matchedAlthough deoxyribose and phosphate arrange stably on thedeoxyribonucleotide long chains the order of base pairs isprotean on the long chain There are only four bases andtwo methods of four types of the four bases to form theDNA molecules but different orders of base pairs constitutea wealth of information [19]
The crossover andmutation inDNAalgorithm is differentfrom genetic algorithm Crossover and mutation in DNAalgorithm is based on gene level with a different encodingmethod which is two digits binary encoding instead of unitbinary encoding The crossover operation of DNA algorithmis based on the two-point crossover method with a certainprobability 119901
119888 which means that a part of bases swaps
randomly in the deoxyribonucleotide long chains to formnew deoxyribonucleotide long chains (see Figure 11)
Transform coding method of DNA algorithm into twobinary coding method can be recognized by computerswhich is A-00 T-01 C-10 G-11 and 00 with 01 and 10 with11 (see Figure 12)
Mutation of DNA algorithm is based on purine replacingpurine and pyrimidine replacing pyrimidine with A chang-ing into G and C changing into T Bases correspond to binarymachines coding method with 00 changing with 11 and10 changing with 01 In the mutation the base sequencesmutation operates in a certain probability 119901
119898(see Figure 13)
DNA-ant colony algorithm optimizes the parameters120572 120573 120588 of the basic ant colony algorithm based on thecrossover and mutation ideas of DNA algorithm to solvethe low carbon logistics route optimization problems Thesolution processes of low carbon logistics route optimizationbased on DNA-ant colony algorithm is as shown in Figure 1The pseudocode of low carbon logistics route optimizationbased on DNA-Ant colony algorithm is as follows
(1) The basic ant colony algorithm parameters initializa-tion is as follows
119873119862 = 0 (119873119862 is the number of iterations)119871119900119886119889 = 0 (119871119900119886119889 is the vehicle load)120591119894119895(0) = 0 (the pheromone on branch 119894119895 is 0)
(2) The DNA ant colony algorithm parameters initializa-tion is as follows
119863119873119860 119873119880119872 = 10 (119863119873119860 119873119880119872 is the numberof updating generation of DNA algorithm)120572(1119873119880119872) (119886 is importancematrix of the resid-ual information)
6 Discrete Dynamics in Nature and Society
yes
No
N
Y
YEnd
N
Initialization ant colony algorithm parameters
Initialization DNA-ant colony algorithmparameters
m ants are on the distribution center
Tabu is full
Calculation of the target function
Cross and mutate
Update the pheromone
Select the optimum NUM2 as parent DNA
Start
Calculation of transition probability select and move on to the next city j and add j to tabu
clear tabu NC = NCmax
NC = NC + 1
Overloaded
Figure 1 The model solution flow chart of DNA-ant colony algorithm
120573(1119873119880119872) (120573 is the importance matrix of theinspiring pheromone)
120588(1119873119880119872) (120588 is the matrix of pheromone vola-tilization coefficient)
119901119888= 06 (119901
119888is the crossover probability of DNA
algorithm)
119901119898= 008 (119901
119898is the mutation probability of
DNA algorithm)
Discrete Dynamics in Nature and Society 7
(3) Operate crossover and mutation of DNA algorithmare as follows
for 1 to119863119873119860 119873119880119872 dorepeat Steps (3)sim(8)operate crossover and mutation of DNA algo-rithmfor 1 to119873119880119872 dorepeat Steps (4)sim(7)
(4) Put 119898 ants at the distribution center The number ofdistribution center 1 in the array tabu to form the arraytabu(1) is as follows
while119873119862 lt 119873119862maxfor 119894 = 1 to119898 do119869 = 1 23 119899 minus tabu(1) (119869 is the matrix of thecities will be visited)
(5) 119896 = 119896 + 1
calculate the transition probability of antsaccording to Formula (28)119871119900119886119889 = 119871119900119886119889 + 119871119900119886119889 119904119890119903V119890119903(119896)if 119871119900119886119889 le 119871119900119886119889 maxant 119894 goes to the next City 119895 Choose and moveto the next City 119895 and put 119895 into array tabuelseant 119894 returns to distribution center and putdistribution center with number 1 into arraytabu119871119900119886119889 = 0repeat Step (5) until all the cities have travelledthrough and then check whether tabu is full Ifnot return to Step (5) Otherwise go on to Step(6)
(6) for 119894 = 1 to119898 do
calculate the path length 119897 to solve the objectivefunction (the values of minimum carbon emis-sions cost function or the objective evaluationfunction) and record the current best solutionUpdate the pheromone based on the formula(25)
(7) if119873119862 lt 119873119862max
119873119862 = 119873119862 + 1 (29)
and then clean up tabu and return to Step (4)
(8) Choose the better 1198731198801198722 as the parent DNA tooperate the crossover and mutation Get the new120572 120573 120588 parameter matrices and return to Step (3)
4 Results and Discussion
Assume the distribution center has 16 customers whosecoordinate is (00) Table 1 is the demand of each customerTable 2 is the coordinate of each customer The maximumload of each vehicle is 75 tons In the simulation set 119888
0=
0 1198881= 1 119888
2= infin The unit distance fuel cost of empty car
and full car is 1205760= 1 and 120576lowast = 2 The unit carbon emissions
cost is 1198883= 03 The emission factor is 120578 = 261 [20] The
distances between each customer and distribution center canbe calculated by Formula (30)
119889119894119895= radic(119909
119894minus 119909119895)
2
+ (119910119894minus 119910119895)
2
(30)
Table 3 shows the 10 results by using the basic ant colonyalgorithm to solve the minimum carbon emissions costmodel Table 4 shows the 10 results by using the DNA-antcolony algorithm to solve the minimum carbon emissionscost model Comparing Table 3 with Table 4 we can find thefollowing
(1) Carbon emissions cost the minimum carbon emis-sions cost of basic ant colony algorithm is 4265and the cost of DNA-ant colony algorithm is 3988The DNA-ant colony algorithm saves 64 of min-imum carbon emissions cost compared with basicant colony algorithm The average carbon emissionscost of basic ant colony algorithm is 5462 Theaverage cost of DNA-Ant colony algorithm is 47034For the average carbon emissions cost the DNA-antcolony algorithm saves 138 comparedwith basic antcolony algorithmThus for the solution of minimumcarbon emissions cost distribution model DNA-antcolony algorithm can find the path with less carbonemissions cost which is better for environmentalprotection
(2) The number of final generation the average numberof final generation of basic ant colony algorithm is1337The average number of final generation of DNA-ant colony algorithm is 81 From the average numberof final generation we can find that the DNA-antcolony algorithm has a better convergence
(3) The difference with minimum carbon emissions costthe average difference between basic ant colonyalgorithm and minimum carbon emissions cost is1197The average difference betweenDNA-ant colonyalgorithm and minimum carbon emissions cost is7154 From the difference with minimum carbonemissions cost we can find that the DNA-Ant colonyalgorithm is more stable in the process of searchminimum carbon emissions
Figure 2 is the distribution path of basic ant colony based ontheminimumcarbon emissions costmodelTheprocesses areas follows
Distribution CenterrarrCustomer13rarrCustomer10rarrCustomer11rarrDistribution Center
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
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6 Discrete Dynamics in Nature and Society
yes
No
N
Y
YEnd
N
Initialization ant colony algorithm parameters
Initialization DNA-ant colony algorithmparameters
m ants are on the distribution center
Tabu is full
Calculation of the target function
Cross and mutate
Update the pheromone
Select the optimum NUM2 as parent DNA
Start
Calculation of transition probability select and move on to the next city j and add j to tabu
clear tabu NC = NCmax
NC = NC + 1
Overloaded
Figure 1 The model solution flow chart of DNA-ant colony algorithm
120573(1119873119880119872) (120573 is the importance matrix of theinspiring pheromone)
120588(1119873119880119872) (120588 is the matrix of pheromone vola-tilization coefficient)
119901119888= 06 (119901
119888is the crossover probability of DNA
algorithm)
119901119898= 008 (119901
119898is the mutation probability of
DNA algorithm)
Discrete Dynamics in Nature and Society 7
(3) Operate crossover and mutation of DNA algorithmare as follows
for 1 to119863119873119860 119873119880119872 dorepeat Steps (3)sim(8)operate crossover and mutation of DNA algo-rithmfor 1 to119873119880119872 dorepeat Steps (4)sim(7)
(4) Put 119898 ants at the distribution center The number ofdistribution center 1 in the array tabu to form the arraytabu(1) is as follows
while119873119862 lt 119873119862maxfor 119894 = 1 to119898 do119869 = 1 23 119899 minus tabu(1) (119869 is the matrix of thecities will be visited)
(5) 119896 = 119896 + 1
calculate the transition probability of antsaccording to Formula (28)119871119900119886119889 = 119871119900119886119889 + 119871119900119886119889 119904119890119903V119890119903(119896)if 119871119900119886119889 le 119871119900119886119889 maxant 119894 goes to the next City 119895 Choose and moveto the next City 119895 and put 119895 into array tabuelseant 119894 returns to distribution center and putdistribution center with number 1 into arraytabu119871119900119886119889 = 0repeat Step (5) until all the cities have travelledthrough and then check whether tabu is full Ifnot return to Step (5) Otherwise go on to Step(6)
(6) for 119894 = 1 to119898 do
calculate the path length 119897 to solve the objectivefunction (the values of minimum carbon emis-sions cost function or the objective evaluationfunction) and record the current best solutionUpdate the pheromone based on the formula(25)
(7) if119873119862 lt 119873119862max
119873119862 = 119873119862 + 1 (29)
and then clean up tabu and return to Step (4)
(8) Choose the better 1198731198801198722 as the parent DNA tooperate the crossover and mutation Get the new120572 120573 120588 parameter matrices and return to Step (3)
4 Results and Discussion
Assume the distribution center has 16 customers whosecoordinate is (00) Table 1 is the demand of each customerTable 2 is the coordinate of each customer The maximumload of each vehicle is 75 tons In the simulation set 119888
0=
0 1198881= 1 119888
2= infin The unit distance fuel cost of empty car
and full car is 1205760= 1 and 120576lowast = 2 The unit carbon emissions
cost is 1198883= 03 The emission factor is 120578 = 261 [20] The
distances between each customer and distribution center canbe calculated by Formula (30)
119889119894119895= radic(119909
119894minus 119909119895)
2
+ (119910119894minus 119910119895)
2
(30)
Table 3 shows the 10 results by using the basic ant colonyalgorithm to solve the minimum carbon emissions costmodel Table 4 shows the 10 results by using the DNA-antcolony algorithm to solve the minimum carbon emissionscost model Comparing Table 3 with Table 4 we can find thefollowing
(1) Carbon emissions cost the minimum carbon emis-sions cost of basic ant colony algorithm is 4265and the cost of DNA-ant colony algorithm is 3988The DNA-ant colony algorithm saves 64 of min-imum carbon emissions cost compared with basicant colony algorithm The average carbon emissionscost of basic ant colony algorithm is 5462 Theaverage cost of DNA-Ant colony algorithm is 47034For the average carbon emissions cost the DNA-antcolony algorithm saves 138 comparedwith basic antcolony algorithmThus for the solution of minimumcarbon emissions cost distribution model DNA-antcolony algorithm can find the path with less carbonemissions cost which is better for environmentalprotection
(2) The number of final generation the average numberof final generation of basic ant colony algorithm is1337The average number of final generation of DNA-ant colony algorithm is 81 From the average numberof final generation we can find that the DNA-antcolony algorithm has a better convergence
(3) The difference with minimum carbon emissions costthe average difference between basic ant colonyalgorithm and minimum carbon emissions cost is1197The average difference betweenDNA-ant colonyalgorithm and minimum carbon emissions cost is7154 From the difference with minimum carbonemissions cost we can find that the DNA-Ant colonyalgorithm is more stable in the process of searchminimum carbon emissions
Figure 2 is the distribution path of basic ant colony based ontheminimumcarbon emissions costmodelTheprocesses areas follows
Distribution CenterrarrCustomer13rarrCustomer10rarrCustomer11rarrDistribution Center
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
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Discrete Dynamics in Nature and Society 7
(3) Operate crossover and mutation of DNA algorithmare as follows
for 1 to119863119873119860 119873119880119872 dorepeat Steps (3)sim(8)operate crossover and mutation of DNA algo-rithmfor 1 to119873119880119872 dorepeat Steps (4)sim(7)
(4) Put 119898 ants at the distribution center The number ofdistribution center 1 in the array tabu to form the arraytabu(1) is as follows
while119873119862 lt 119873119862maxfor 119894 = 1 to119898 do119869 = 1 23 119899 minus tabu(1) (119869 is the matrix of thecities will be visited)
(5) 119896 = 119896 + 1
calculate the transition probability of antsaccording to Formula (28)119871119900119886119889 = 119871119900119886119889 + 119871119900119886119889 119904119890119903V119890119903(119896)if 119871119900119886119889 le 119871119900119886119889 maxant 119894 goes to the next City 119895 Choose and moveto the next City 119895 and put 119895 into array tabuelseant 119894 returns to distribution center and putdistribution center with number 1 into arraytabu119871119900119886119889 = 0repeat Step (5) until all the cities have travelledthrough and then check whether tabu is full Ifnot return to Step (5) Otherwise go on to Step(6)
(6) for 119894 = 1 to119898 do
calculate the path length 119897 to solve the objectivefunction (the values of minimum carbon emis-sions cost function or the objective evaluationfunction) and record the current best solutionUpdate the pheromone based on the formula(25)
(7) if119873119862 lt 119873119862max
119873119862 = 119873119862 + 1 (29)
and then clean up tabu and return to Step (4)
(8) Choose the better 1198731198801198722 as the parent DNA tooperate the crossover and mutation Get the new120572 120573 120588 parameter matrices and return to Step (3)
4 Results and Discussion
Assume the distribution center has 16 customers whosecoordinate is (00) Table 1 is the demand of each customerTable 2 is the coordinate of each customer The maximumload of each vehicle is 75 tons In the simulation set 119888
0=
0 1198881= 1 119888
2= infin The unit distance fuel cost of empty car
and full car is 1205760= 1 and 120576lowast = 2 The unit carbon emissions
cost is 1198883= 03 The emission factor is 120578 = 261 [20] The
distances between each customer and distribution center canbe calculated by Formula (30)
119889119894119895= radic(119909
119894minus 119909119895)
2
+ (119910119894minus 119910119895)
2
(30)
Table 3 shows the 10 results by using the basic ant colonyalgorithm to solve the minimum carbon emissions costmodel Table 4 shows the 10 results by using the DNA-antcolony algorithm to solve the minimum carbon emissionscost model Comparing Table 3 with Table 4 we can find thefollowing
(1) Carbon emissions cost the minimum carbon emis-sions cost of basic ant colony algorithm is 4265and the cost of DNA-ant colony algorithm is 3988The DNA-ant colony algorithm saves 64 of min-imum carbon emissions cost compared with basicant colony algorithm The average carbon emissionscost of basic ant colony algorithm is 5462 Theaverage cost of DNA-Ant colony algorithm is 47034For the average carbon emissions cost the DNA-antcolony algorithm saves 138 comparedwith basic antcolony algorithmThus for the solution of minimumcarbon emissions cost distribution model DNA-antcolony algorithm can find the path with less carbonemissions cost which is better for environmentalprotection
(2) The number of final generation the average numberof final generation of basic ant colony algorithm is1337The average number of final generation of DNA-ant colony algorithm is 81 From the average numberof final generation we can find that the DNA-antcolony algorithm has a better convergence
(3) The difference with minimum carbon emissions costthe average difference between basic ant colonyalgorithm and minimum carbon emissions cost is1197The average difference betweenDNA-ant colonyalgorithm and minimum carbon emissions cost is7154 From the difference with minimum carbonemissions cost we can find that the DNA-Ant colonyalgorithm is more stable in the process of searchminimum carbon emissions
Figure 2 is the distribution path of basic ant colony based ontheminimumcarbon emissions costmodelTheprocesses areas follows
Distribution CenterrarrCustomer13rarrCustomer10rarrCustomer11rarrDistribution Center
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
8 Discrete Dynamics in Nature and Society
Table 1 Demand of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Demand 15 18 20 8 15 10 25 30 17 6 2 24 19 20 7 1
Table 2 Coordinate of customer
Customer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16119883 2 8 18 34 minus25 35 42 minus10 minus8 minus12 minus32 28 minus18 minus9 minus18 8119884 8 33 20 28 15 minus5 10 20 10 minus32 minus40 7 0 25 8 10
Table 3 The results of basic ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5723 5441 5809 5926 5725 5442 5207 5599 5483 4265 5462Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 68 180 144 140 188 79 193 182 67 96 1337Deviations 1458 1176 1544 1661 146 1177 942 1334 1218 0 1197
Table 4 The results of DNA-ant colony algorithm (minimum carbon emissions cost)
No 1 2 3 4 5 6 7 8 9 10 AveCarbon emissions cost 5162 4446 4936 4891 4613 4844 4564 4853 4737 3988 47034Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 174 144 79 16 16 46 65 175 34 61 81Deviations 1174 458 948 903 625 856 576 865 749 0 7154
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40 Ant colony algorithm
6
7
4
121 163
214
9
8
5
15
13
1011
Distribution center
Figure 2 Distribution path basic ant colony algorithm (minimumcarbon emissions cost)
Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution Center
Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution Center
Distribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution Center
Figure 3 is the distribution path ofDNA-Ant colony basedon theminimum carbon emissions cost modelThe processesare as follows
Distribution CenterrarrCustomer10rarrCustomer11rarrCustomer13rarrDistribution CenterDistribution CenterrarrCustomer6rarrCustomer7rarrCustomer4rarrCustomer12rarrDistribution CenterDistribution CenterrarrCustomer8rarrCustomer14rarrCustomer5rarrCustomer15rarrDistribution CenterDistribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer9rarrDistribution Center
Figure 4 is the optimization curves of minimum carbonemissions cost From the figure we can find that DNA-Antcolony algorithm has a better effectiveness in the process ofsearching minimum carbon emissions cost Comparing withbasic ant colony algorithm we can find the lower carbonemissions cost with a faster convergence speed
When the air pollution level is good level vehiclesare only considered the distribution cost and the carbonemissions cost is ignored which means that 120588
1= 0 120588
2= 1
At this time the minimum value of objective function is theminimum value of distribution cost
Table 5 shows the 10 results by using the basic ant colonyalgorithm to solve the double targets distribution optimi-zation model under the top or good air pollution levelcondition Table 6 shows the 10 results by using the DNA-ant colony algorithm to solve the double targets distribution
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Discrete Dynamics in Nature and Society 9
Table 5 The results of basic ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 4031 4027 4039 4045 4075 4053 4007 4053 4095 4079 40504Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 186 159 125 15 178 123 196 5 63 63 1113Deviations 24 2 32 38 68 46 0 46 88 72 434
Table 6 The results of DNA-ant colony algorithm (top or good air pollution level)
No 1 2 3 4 5 6 7 8 9 10 AveCost 400 398 4007 398 398 404 398 4007 398 4079 40033Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 19 145 77 13 33 16 16 163 27 27 536Deviations 2 0 27 0 0 6 0 27 0 99 233
DNA-ant colony algorithm
6
7
4
121 16
3
2
9
1011
1315
5
14
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 3 Distribution path DNA-ant colony algorithm (minimumcarbon emissions cost)
0 50 100 150 200390
400
410
420
430
440
450
460
DNA-ant colony algorith
DNA-ant colony algorithm
m
Ant colony algorithm
Ant colony algorithm
X 61
X 96Y 4265
Y 3988
Figure 4 Minimum carbon emissions cost optimization curve
optimization model under the top or good air pollution levelcondition Comparing Table 5 with Table 6 we can find thefollowing
(1) Distribution cost the minimum distribution cost ofbasic ant colony algorithm is 4007 and the costof DNA-ant colony algorithm is 398 The DNA-antcolony algorithm saves 067 of minimum distribu-tion cost comparing with basic ant colony algorithmThe average distribution cost of basic ant colony algo-rithm is 40504 The average cost of DNA-ant colonyalgorithm is 40033 For the average distribution costthe DNA-ant colony algorithm saves 116 comparedwith basic ant colony algorithmThus for the good airpollution level DNA-ant colony algorithm can findthe path with less distribution cost compared withbasic ant colony algorithm
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1113 The average number of final generation ofDNA-ant colony algorithm is 536 From the averagenumber of final generation we can find the DNA-antcolony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 434 The average difference betweenDNA-ant colony algorithm and minimum values is233 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 5 is the distribution path figure of basic ant colonyalgorithm which is shown in Table 7 Figure 6 is the distri-bution path figure of DNA-Ant colony algorithm which isshown in Table 8
Figure 7 is the distribution cost optimization curves com-paring the figure of the two algorithms From the simulationwe can find that DNA-ant colony algorithm performances ismore effective on the solution issue which can save moredistribution cost with a faster convergence speed
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
10 Discrete Dynamics in Nature and Society
Ant colony algorithm
12
6
7
4
1011
13
1 163
214
915
5
8
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 5 Distribution path basic ant colony algorithm (top or goodair pollution level)
DNA-ant colony algorithm
1011
13 12
6
7
4
9
8
5
151 16
32
14
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
0
10
20
30
40
Figure 6Distribution pathDNA-ant colony algorithm (top or goodair pollution level)
Table 7 The distribution path figure of basic ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash10ndash11ndash13ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash15ndash5ndash8ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
Table 8The distribution path figure of DNA-ant colony algorithm
Vehicle 119896 Distribution path1 Distribution Centerndash13ndash11ndash10ndashDistribution Center2 Distribution Centerndash1ndash16ndash3ndash2ndash14ndashDistribution Center3 Distribution Centerndash9ndash8ndash5ndash15ndashDistribution Center4 Distribution Centerndash12ndash6ndash7ndash4ndashDistribution Center
0 50 100 150 200395
400
405
410
415
420
425
430
DNA-ant colony algorithm
Ant colony algorithm
DNA-ant colony algorithmAnt colony algorithm
X 16X 196
Y 4007Y 398
Figure 7 Distribution cost optimization curve (top or good air pol-lution level)
Assume that the air pollution level is moderate or highlevel pollution set 120588
1= 08 120588
2= 02 Table 9 shows the
10 results by using the basic ant colony algorithm to solvethe double targets distribution optimizationmodel under themoderate or high level pollution condition Table 10 showsthe 10 results by using the DNA-ant colony algorithm to solvethe double targets distribution optimization model underthe moderate or high level pollution condition ComparingTable 9 with Table 10 we can find the following
(1) Objective evaluation function value the minimumobjective evaluation function value of basic ant colonyalgorithm is 4175 and the cost of DNA-ant colonyalgorithm is 4026 The DNA-ant colony algorithmsaves 35 of minimum objective evaluation functionvalue compared with basic ant colony algorithm Theaverage objective evaluation function value of basicant colony algorithm is 43122 The average cost ofDNA-ant colony algorithm is 41409 For the averageobjective evaluation function value the DNA-antcolony algorithm saves 397 compared with basicant colony algorithm Thus for the moderate or highlevel pollution DNA-ant colony algorithm can findthe path with less objective evaluation function valueto find the more effective distribution paths andreduce air pollution and distribution cost
(2) The number of final generation the average numberof final generation of basic ant colony algorithmis 1633 The average number of final generation ofDNA-ant colony algorithm is 869 From the averagenumber of final generation we can find that theDNA-ant colony algorithm has a better convergence speed
(3) The difference with minimum values the average dif-ference between basic ant colony algorithm and min-imum values is 1372 The average difference betweenDNA-ant colony algorithm and minimum values is
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Discrete Dynamics in Nature and Society 11
Table 9 The results of basic ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4303 4224 4175 4232 4584 4332 4434 4374 4184 428 43122Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 160 175 193 150 155 162 182 161 163 132 1633Deviations 128 49 0 57 409 157 259 199 09 105 1372
Table 10 The results of DNA-ant colony algorithm (moderate or high level pollution)
No 1 2 3 4 5 6 7 8 9 10 AveW 4186 4026 4026 409 4126 4287 4148 4211 4158 4151 41409Vehicles 4 4 4 4 4 4 4 4 4 4 4End iteration 126 30 133 68 20 133 26 46 131 156 869Deviations 16 0 0 64 10 261 122 185 132 125 1149
Ant colony algorithm
13
1110
9
8
5
15
16 3
4214
1 127
6Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 8 Distribution path basic ant colony algorithm (moderateor high level pollution)
1149 From the difference with minimum values wecan find that the DNA-ant colony algorithm is morestable in the process of search the best solution
Figure 8 is the distribution path of basic ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer13rarrCustomer11rarrCustomer10rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer9rarrCustomer8rarrCustomer5rarrCustomer15rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer16rarrCustomer3rarrCustomer4rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer1rarrCustomer12rarrCustomer6rarrCustomer7rarrDistribution Center
DNA-ant colony algorithm
9 12
4
7
6
1011
13
15
58
116
3
214
Distribution center
minus40 minus30 minus20 minus10 0 10 20 30 40 50minus40
minus30
minus20
minus10
10
20
30
40
0
Figure 9 Distribution path DNA-ant colony algorithm (moderateor high level pollution)
0 50 100 150 200400
405
410
415
420
425
430
435
440
DNA-ant colony algorithmAnt colony algorithm
DNA-ant colony algorithm
Ant colony algorithmX 193Y 4175
X 133Y 4026
Figure 10 Distribution cost optimization curve (moderate or highlevel pollution)
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
12 Discrete Dynamics in Nature and Society
Ancestral DNA ACTCG||TGCCA GTAC||GTGACAGACCT||AGGAT CAGT||TCGAAC
CrossACTCG||AGGAT CAGT||TCGAACGACCT||TGCCA GTAC||GTGACA
Filial generation DNA
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 11
Ancestral DNA 00 10 01 10 11||01 11 10 10 00 11 01 00 10||11 01 11 00 10 0011 00 10 10 01||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
CrossFilial generation 00 10 01 10 11||00 11 11 00 01 10 00 11 01||01 10 11 00 00 10
11 00 10 10 01||01 11 10 10 00 11 01 00 10||11 01 11 00 10 00
middot middot middot
middot middot middot
middot middot middot
middot middot middotDNA
Figure 12
Ancestral DNA TAGGC||CAAGT CTGA||CAGATCMutate
Filial generation DNA TAGGC|| CAAGC CTGA||CAGATCAncestral DNA 01 00 11 11 10||10 00 00 11 01 10 01 11 00||10 00 11 00 01 10
MutateFilial generation DNA 01 00 11 11 10||10 00 00 11 10 10 01 11 00||10 00 11 00 01 10
middot middot middot
middot middot middot
middot middot middot
middot middot middot
Figure 13
Figure 9 is the distribution path ofDNA-ant colony undermoderate or high level pollution conditionThe processes areas follows
Vehicle 1 Distribution CenterrarrCustomer1rarrCustomer16rarrCustomer3rarrCustomer2rarrCustomer14rarrDistribution CenterVehicle 2 Distribution CenterrarrCustomer13rarrCustomer15rarrCustomer5rarrCustomer8rarrDistribution CenterVehicle 3 Distribution CenterrarrCustomer12rarrCustomer4rarrCustomer7rarrCustomer6rarrCustomer10rarrCustomer11rarrDistribution CenterVehicle 4 Distribution CenterrarrCustomer9rarrDistribution Center
Figure 10 is the optimization curve of objective evaluationfunction best value From the figure we can find that underthe moderate or high level pollution condition DNA-antcolony algorithm can find the lower objective evaluationfunction value to get a faster convergence speed than the basicant colony algorithm
5 Conclusions
In this paper starting from the actual requirements of lowcarbon logistics microscopic quantitative analysis was usedfor low carbon logistics The minimum cost of carbon emis-sions model and the double target distribution optimizationmodel with considering the cost of carbon emissions were
established to find the reasonable distribution routes toachieve energy conservation and emissions reduction basedon the solution of DNA-ant colony algorithm According tothe simulation ofMATLABDNA-ant colony algorithmhad abetter effectiveness than the basic ant colony algorithmon theissue of low carbon logistics distribution route optimizationBut this is the preliminary research on the low carbonlogistics distribution route optimization problem It is theexploration stage for low carbon logistics distribution routeoptimization model The models are established based onthe ideal situation without consideration of many complexfactors and real situations in the constraints of the modelsIn future study there is a to optimize the model to make themodel more accord with the actual needs
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
This work was supported by Soft Science Research Project inShanxi Province (no 2010041077-3)
References
[1] X Xu ldquoResearch on construction and characteristics of lowcarbon logistics systemrdquo Commercial Times no 10 pp 23ndash242011
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Discrete Dynamics in Nature and Society 13
[2] X-Y Liu ldquoAnalysis of the development of low-carbon logisticsbased on a low-carbon economyrdquo in Proceedings of the Interna-tional Conference on Low-Carbon Transportation and Logisticsand Green Buildings pp 673ndash679 2013
[3] H-J Wu and S Dunn ldquoEnvironmentally responsible logistiessystemsrdquo International Journal of Physical Distribution andLogistics Management vol 25 no 2 pp 20ndash38 1995
[4] J P Rodrigue B Slake and C Comtois ldquoGreen logisticsrdquo inTheHandbook of Logistics and Supply-Chain Management A MBrewer K J Button and D A Hensher Eds Paragon ElsevierLondon UK 2001
[5] A McKinnon ldquoGreen logistics the carbon agendardquo ElectronicScientific Journal of Logistics vol 6 no 3 pp 1ndash9 2010
[6] J Liu and K Han ldquoEstablishment of logistics system in low-carbon economyrdquo Logistics Technology no 13 pp 77ndash79 2013
[7] X Lin ldquoChina-ASEAN and Guangxi multiple-regions coop-erative low-carbon logistics internet of things service systemhidden Markov optimization modelrdquo Advances in Intelligentand Soft Computing vol 162 pp 65ndash72 2012
[8] M Yang and Y Tian ldquoEstablishment and application of logisticsenterpriseslow-carbon factors index systemrdquo in Proceedings ofthe 2nd International Conference on Logistics Informatics andService Science (LISS 12) pp 401ndash407 July 2012
[9] S Cholette and K Venkat ldquoThe energy and carbon intensityof wine distribution a study of logistical options for deliveringwine to consumersrdquo Journal of Cleaner Production vol 17 no16 pp 1401ndash1413 2009
[10] I Harris M Naim A Palmer A Potter and C MumfordldquoAssessing the impact of cost optimization based on infras-tructure modelling on CO
2emissionsrdquo International Journal of
Production Economics vol 131 no 1 pp 313ndash321 2011[11] Y Wang T Lu and C Zhang ldquoIntegrated logistics network
design in hybridmanufacturingremanufacturing systemunderlow-carbon restrictionrdquo in Proceedings of the 2nd InternationalConference on Logistics Informatics and Service Science (LISS12) pp 111ndash121 July 2012
[12] H Huang ldquoA study of developing Chinese low carbon logisticsin the new railway periodrdquo in Proceedings of the InternationalConference on E-Product E-Service and E-Entertainment (ICEEE10) pp 635ndash638 November 2010
[13] S Qin Research on fuel consumption minimized vehicle routingproblem [MS thesis] Tsinghua University Beijing China 2011
[14] Y Le and P Zhen ldquoPath design of emergency medical suppliestransportrdquo Logistics Technology vol 27 no 11 pp 84ndash86 2008
[15] M Dorigo and L M Gambardella ldquoAnt colony system a coop-erative learning approach to the traveling salesman problemrdquoIEEETransactions on Evolutionary Computation vol 1 no 1 pp53ndash66 1997
[16] C Wu DNA algorithm of the minimum set covering problemin wireless sensor networks research [MS thesis] East ChinaUniversity of Science and Technology Shanghai China 2010
[17] X Chen DNA genetic algorithm and its application [PhDthesis] Zhejiang University Zhejiang China 2010
[18] R J Lipton ldquoDNA solution of hard computational problemsrdquoScience vol 268 no 5210 pp 542ndash545 1995
[19] H Zhu Vehicles scheduling problemwith DNA algorithmresearch [MS thesis] Harbin University of Science and Tech-nology Harbin China 2003
[20] L V Pin ldquoStudy of logistics network optimization model con-sidering carbon emissionsrdquo Application Research of Computersvol 30 no 10 pp 2977ndash2980 2013
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of