research article multiconstrained qos routing using a...

Research ArticleMulticonstrained QoS Routing Using a Differentially GuidedKrill Herd Algorithm in Mobile Ad Hoc Networks

D Kalaiselvi1 and R Radhakrishnan2

1Computer Science amp Engineering Jay Shriram Group of Institutions Tiruppur 638 660 India2Sri Shakthi Institute of Engineering amp Technology Coimbatore 641 062 India

Correspondence should be addressed to D Kalaiselvi kalai tabuyahoocom

Received 6 February 2014 Revised 29 May 2014 Accepted 28 July 2014

Academic Editor Albert Victoire

Copyright copy 2015 D Kalaiselvi and R Radhakrishnan This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

This paper presents a multiconstrained quality-of-service routing (QoSR) based on a differentially guided krill herd (DGKH)algorithm in mobile ad hoc networks (MANETs) QoSR is a NP-complete and significant problem with immense challenges indetermining an optimum path that simultaneously satisfies various constraints in MANETs where the topology varies constantlyVarious heuristic algorithms are widely used to solve this problem with compromise on excessive computational complexitiesandor low performanceThis paper proposes a krill herd based algorithm called DGKH where the krill individuals do not updatethe position in comparison with one-to-one (as usual) but instead it uses the information from various krill individuals andthen searches to determine a feasible path Experiment results on MANETs with different number nodes (routes) are consideredwith three constraints which are maximum allowed delay maximum allowed jitter and minimum requested bandwidth It isdemonstrated that the proposedDGKHalgorithm is an effective approximation algorithm exhibiting satisfactory performance thanthe KHA and existing algorithms in the literature by determining an optimum path that satisfies more than one QoS constraint inMANETs

1 Introduction

Mobile ad hoc networks (MANETs) are class of wirelesscommunication networks without a fixed infrastructure TheMANET nodes do not provide reliable services and QoS(quality of service) guarantees as compared to other wirelessnetworks such as WiFi WiMAX GSM and CDMA [1]The QoS parameters to be guaranteed for multimedia groupcommunication are bandwidth delay packet loss rate jittersand bandwidth-delay product QoS is one of the significantcomponents to evaluate MANET performance since QoSrestricts the bounds on bandwidth delay bandwidth delayproduct jitter and packet loss [2 3] The violation ofthese parameters degrades the overall performance of anapplication

Its primary goal is to allocate network resources effi-ciently while the different QoS requirements are satisfiedsimultaneously The QoS requirements can be classified intolink constraints (eg band width) path constraints (egend to end delay) and tree constraints (eg delay-jitter)

The interdependency and confliction among multiple QoSparameters however make the problem very difficult andNP-complete [4 5] For the reason that the QoS multicastrouting problem is NP-complete several heuristic algorithmshave been deployed to address this problem For examplesimulated annealing (SA) a powerful global optimizationprocedure was utilized to solve theQoSRproblem [6]Unlikeother heuristic techniques SA involves single candidate tosearch for the solution thatmake themethod inefficient whilesolving large dimension problems

Subsequently another powerful population based tech-nique called genetic algorithms (GAs) has been engaged tosolve the QoSR problem [7ndash9] GA assures a larger possi-bility of locating a global optimum by starting with multi-ple random search points and processing several candidatesolutions simultaneously Perhaps it is always criticizedthat genetic algorithms encounters some faults such as lackof local search ability premature convergence and slowconvergence speed Similarly due to the advent of swarmintelligence theory a category of stochastic search methods

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 862145 10 pageshttpdxdoiorg1011552015862145

2 Mathematical Problems in Engineering

for solving optimization (GO) problems of NP nature antcolony optimization (ACO) and particle swarmoptimization(PSO) is introduced

Similar to GA these two methods were also shown tobe efficient tools for solving the multicast routing problem[10ndash13] In [10 11] theQoS-multiple constrained optimizationproblem has been solved using ant colony optimization(ACO) algorithm Here the authors examined the degree anddelay-constrained broadcasting problem with minimum costusing an ant colony-based algorithm After simulations andcomparisons with previous ant algorithm and to two GA-based algorithms the obtained results exhibited the best costbut again with too long computation time

Consequently PSO [12 13] was also used to addressthe QoSR problem PSO can be easily implemented andis computationally inexpensive since its memory and CPUspeed requirements are low PSO has been proved to be anefficient approach for many optimization problems with itsfast convergence and simple steps to solve a problem In spiteof these merits a known fact that PSO has a severe drawbackin the update of its global best (gbest) particle which has acrucial role of guiding the rest of the particles this leads toovercoming better solutions in the course of search

In row of these heuristics another new metaheuristiccalled Bees Life Algorithm (BLA) is proposed [14] As oneof the specie colony optimization BLA is considered asa swarm intelligence algorithm and an approximate opti-mization method which performs according to collaborativeindividual behaviors in the population But still like otherprobabilistic optimization algorithms BLA has inherentdrawback of premature convergence or stagnation that leadsto loss of exploration and exploitation capability In line tothis other heuristics like tabu search [15] and harmony searchalgorithm [16] were proposed for QoSR with minimumnumber of constraints

In fact there is a growing body of literature in theapplication of emerging heuristics to solve theNP-hardQoSRproblemThis paper proposes a krill herd based algorithm forQoSR in MANETS Krill herd algorithm (KHA) is a recentlydeveloped powerful evolutionary algorithm proposed byGandomi and Alavi [17] The KHA is based on the herdingbehavior of krill individuals Each krill individual modifiesits position using three processes namely (1) movementinduced by other individuals (2) foraging motion and (3)

random physical diffusion The motion induced by otherindividuals and foraging motion contain global and localstrategies respectively which make KHA a powerful tech-niqueHowever sometimes KHA is unable to generate globaloptimal solutions on some high-dimensional nonlinear opti-mization problems

Thus this paper proposes a differentially guided krillherd (DGKH) algorithm where the krill individuals do notupdate the position in comparisonwith one-to-one (as usual)instead it uses the information from various krill individualsand then searches to determine a feasible path Thus theinduction stage uses the position information from variouskrill individuals at random making the search exhaustiveand leads to quick search of better solutions

The rest of the paper is organized as follows In Section 2the problem statement of QoS routing problem in MANETSis introduced The overview of KHA is briefly explainedin Section 3 with description of the proposed differentialguiding mechanism Section 4 presents the numerical exper-iments with a standard QoS multicast routing problem Adetailed discussion about the proposedmethod in theoreticalperspective is detailed in Section 5The paper is concluded inSection 6

2 Problem Statement

Let 119866 = (119881 119864) be an undirected graph representing thenetwork topology where 119881 is the set of nodes and 119864 is theset of links The source node and the multicast destinationnode set containing 119903 destinations are the routes for multicast[18] The end-to-end QoS requirements are expressed asconstraints from the source to the destinations and are givenby the following

The delay (DL) is themaximumdelay along any branch of thetree A penalty is added if no link is found between two nodesConsider

119863 (119901 (119904 119905)) = sum119890isin119901(119904119905)

delay (119890) + sum119899isin119901(119904119905)

delay (119899) (1)

The bandwidth (BW) of the multicast tree is the averagebandwidth requirement of all the tree branches Consider

119861 (119901 (119904 119905)) = min (bandwidth (119890)) 119890 isin 119901 (119904 119905) (2)

The delay-jitter (DJ) is the maximum delay variation alongany branch of the tree Consider

DJ (119901 (119904 119905)) = sum119890isin119901(119904119905)

delay jitter (119890) + sum119899isin119901(119904119905)

delay jitter (119899)

(3)

The packet loss rate is the average packet loss along the treebranchesThe cutoff for PLR is set at 10 If a branch is havingmore than 10 packet loss then a penalty is assigned suchthat the model tries to search a path less than 10 PLR

PL (119901 (119904 119905)) = 1 minus prod119899isin119901(119904119905)

(1 minus packet loss (119899)) (4)

The above QoS criteria have to be fulfilled with an objectiveto minimize cost function of the multicast tree as given by

119862 (119879 (119904 119872)) = sum119890isin119879(119904119872)

cos 119905 (119890) + sum119899isin119879(119904119872)

cos 119905 (119899) (5)

Thus the QoS routing problem is formulated as an optimiza-tion problem whose goal is to find a multicast tree 119879(119904 119872)

Mathematical Problems in Engineering 3

such that the cost function 119862(119879(119904 119872)) is minimized subjectto the constraints as follows

Minimize 119862 (119879 (119904 119872))

st D (119901 (119904 119879)) le QD

B (119901 (119904 119879)) ge QB

DJ (119901 (119904 119879)) le QDJ

PL (119901 (119904 119879)) le QPL

(6)

Subsequently the fitness function is defined as the sum of thecost function and penalized constraints as follows

Minimize 119891 (119879 (119904 119872))

= 119891119888

+ 1205961119891119887

+ 1205962119891119889

+ 1205963119891dj + 120596

4119891pl

(7)

where119891119888

= cos 119905 (119879 (119904 119872))

119891119887

= sum119905isin119872

max QB minus B (119901 (119904 119905)) 0

119891119889

= sum119905isin119872

max D (119901 (119904 119905)) minus QD 0

119891dj = sum119905isin119872

max DJ (119901 (119904 119905)) minus QJ 0

119891pl = sum119905isin119872

max PL (119901 (119904 119905)) minus QPL 0

(8)

where QD is delay constraint QB is bandwidth constraintQDJ is delay-jitter constraint and QPL is packet loss con-straint Also 120596

1 1205962 1205963 1205964 are the weights of bandwidth

delay delay-jitter and packet loss respectively In the nextsection the solution methodology to solve the multicast QoSrouting problem is explained in detail

3 Proposed Methodology

31 Krill Herd Algorithm An Overview Krill herd algorithm(KHA) is a recently developed heuristic algorithm based onthe herding behavior of krill individuals It has been firstproposed by Gandomi and Alavi [17] It is a population basedmethod consisting of a large number of krill in which eachkrill moves through a multidimensional search space to lookfor food In this optimization algorithm the positions ofkrill individuals are considered as different design variablesand the distance of the food from the krill individual isanalogous to the fitness value of the objective functionIn KHA the individual krill alters its position and movesto the better positions The movement of each individualis influenced by the three processes namely (i) inductionprocess (ii) foraging activity and (iii) random diffusionThese operators are briefly explained and mathematicallyexpressed as follows

(i) Induction In this process the velocity of each krill isinfluenced by the movement of other krill individuals of the

multidimensional search space and its velocity is dynamicallyadjusted by the local target and repulsive vectorThe velocityof the 119894th krill at the 119898th movements may be formulated asfollows [17]

V119898119894

= 120572119894Vmax119894

+ 120596119899V119898minus1119894

(9)

120572119894=

119873119878

sum119895=1

[119891119894minus 119891119895

119891119908

minus 119891119887

times119885119894minus 119885119895

10038161003816100381610038161003816119885119894minus 119885119895

10038161003816100381610038161003816+ rand (0 1)

]

+ 2 [rand (0 1) +119894

119894max] 119891

best119894

119885best119894

(10)

where 119881max119894

is the maximum induced motion 119881119898119894

and 119881119898minus1119894

are the inducedmotion of the 119894th krill at the119898th and (119898minus1)thmovement 120596

119899is the inertia weight of the motion induced

119891119908and 119891

119887are the worst and the best position respectively

among all krill individuals of the population 119891119894 119891119895are the

fitness value of the 119894th and 119895th individuals respectively 119873119878

is the number of krill individuals surrounding the particularkrill 119894 and 119894max are the current iteration and the maximumiteration number

A sensing distance (SDi) parameter is used to identify theneighboring members of each krill individual If the distancebetween the two krill individuals is less than the sensingdistance that particular krill is considered as neighbor of theother krill The sensing distance may be represented by [17]

SD119894=

1

5119899119901

119899119901

sum119896=1

1003816100381610038161003816119885119894 minus 119885119896

1003816100381610038161003816 (11)

where 119899119901is the population size 119885

119894and 119885

119896are the position of

the 119894th and 119896th krill respectively

(ii) Foraging Action Each individual krill updates its foragingvelocity according to its own current and previous foodlocation The foraging velocity of the 119894th krill at the 119898thmovement may be expressed by [17]

119881119898

119891119894

= 002 [2 (1 minus119894

119894max) 119891119894

sum119873119878

119896=1(119885119896119891119896)

sum119873119878

119896=1(1119891119896)

+ 119891best119894

119883best119894

]

+ 120596119909119881119898minus1

119891119894

(12)

where 120596119883is the inertia weight of the foraging motion 119881119898minus1

119891119894

and119881119898119891119894

are the foragingmotion of the 119894th krill at the (119898minus1)thand 119898 movement

(iii) Random Diffusion In KHA algorithm in order toenhance the population diversity random diffusion processis incorporated in krill individuals This process maintainsor increases the diversity of the individuals during the wholeoptimization process The diffusion speed of krill individualsmay be expressed as follows [17]

V119898119863119894

= 120583Vmax119863

(13)


where119881max119863

is themaximumdiffusion speed120583 is a directionalvector uniformly distributed between (minus1 1)

(iv) Position Update In KHA the krill individuals fly aroundin the multidimensional space and each krill adjusts itsposition based on induction motion foraging motion anddiffusion motion In this way KHA combines local searchwith global search for balancing the exploration and exploita-tionThe updated position of the 119894th krill may be expressed as[17]

119885119898+1

119894= 119885119898

119894+ (119881119898

119894+ 119881119898

119891119894

+ 119881119898

119863119894

) 119875119905

119873119889

sum119895=1

(119906119895

minus 119897119895) (14)

where 119873119889is the number of control variables 119906

119895and 119897119895are the

maximum andminimum limits of the 119895th control variable 119875119905

is the position constant factor The above procedure will beused to optimize (7) for MANET routing optimization

32 Differentially Guided Procedure This procedure is incor-porated in the movement induced by other krill individualsIn the original KHA the velocity of the 119894th krill at the119898th run is given in (10) The vectors show the induceddirections by different neighbors and each value presents theeffect of a neighbor The neighborsrsquo vector can be attractiveor repulsive since the normalized value can be negativeor positive For choosing the neighbor in original KHA asensing distance (SD

119894) is adopted Instead of such choice

where the krill individuals update the position in compar-ison with one-to-one (as in original KHA) this researchproposes a new mechanism whence the induction stage usesthe position information from various krill individuals atrandom

Differential Guiding Mechanism All krill individuals cangenerate new positions in the search space using the infor-mation derived from different krill individualsrsquo using bestinformation To ensure that a krill individual learns fromgood exemplars and to minimize the time wasted on poordirections we allow the krill individual to learn from theexemplars until the krill individual ceases improving for acertain number of generations called the refreshing gap Weobserve threemain differences between theDGKHalgorithmand the original KHA [17]

(1) Once the sensing distance is used to identify theneighboring members of each krill individual asexemplars to update the position thismechanismuti-lizes the potentials of all krill individualsas exemplarsto guide a krill individualrsquos new position

(2) Instead of learning from the same exemplar krillindividualrsquos for all dimensions each dimension of akrill individual in general can learn from differentkrill individuals for different dimensions to updateits position In other words each dimension of akrill individual may learn from the correspondingdimension of different krill individual based on theproposed equation (15)

(3) Finding the neighbor for different dimensions toupdate a krill individual position is done randomly(with a vigil that repetitions are avoided) Thisimproves the thorough exploration capability of theoriginal KHA with large possibility to avoid prema-ture convergence in complex optimization problems

Compared to the original KHA DGKH algorithm searchesmore promising regions to find the global optimum Thedifference between KHA and DGKH is that the differentialoperator applied to only accept the basicKHAgenerating newbetter solution for each krill instead of accepting all the krillupdating adopted in KH This is rather greedy The originalKHA is very efficient and powerful but is highly proneto premature convergence Therefore to evade prematureconvergence and further improve the exploration ability ofthe original KHA a differential guidance is used to tap usefulinformation in all the krill individuals to update the positionof a particular krill individual The following expresses thedifferential mechanism

119885119894minus 119885119895

= (1199111198941

1199111198942

1199111198943

sdot sdot sdot 119911119894119899

) minus (1199111205881

1199111205882

1199111205883

sdot sdot sdot 119911120588119899

)

(15)

where 1199111198941is the first element in the 119899 dimension vector 119885

119894 119911119894119899

is the 119899th element in the 119899 dimension vector119885119894 1199111205881is the first

element in the 119899 dimension vector 119885119901 and 120588 is the random

integer generated separately for each 119911 between 1 to 119899 but120588 = 119894

Figure 1 shows the differential mechanism for choosingthe neighbor krill individual for (10) This assumes that thedimension of the problem as 5 and assumes krill size as6 are in the search Once the neighbor krill individualsare identified using the sensing distance the 119894th individualposition will be updated (with all neighbor krill individuals)as shown in Figure 1 This is in an effort to avoid prematureconvergence and explore a large promising region in the priorrun phase to search the whole space extensively

4 Experimental Analysis

Numerical Simulations were carried out to validate theperformance of the proposed DGKH based QoSR algorithmand experimental analysis is performed on a test network[12] as shown in Figure 2 on three different cases For Case(1) constraint Set1 delay constraint QD = 20 delay-jitterconstraint QDJ = 30 and bandwidth constraint QB = 40In Case (2) constraint Set2 delay constraint QD = 25 delay-jitter constraint QDJ = 35 and bandwidth constraint QB =

40 In Case (3) in addition to the constraints Set 2 packet lossrate constraints are also taken into account For the packetloss rate constraint we set QPL = 30 as used in [4] sincead hoc networks are high mobility networks with limitedresources Also considering all these parameters can indicatetimeliness and precision which is used to measure the outputperformances of a routing algorithm

First two cases are studied to establish the superiorityof the proposed DGKH based QoSR in comparison to theexisting QPSO method The proposed DGKH algorithm was


ith individual jth individual

Dim

ensio

n

Z11 Z11 Z12 Z13 Z14 Z15 Z16

Z21 Z21 Z22 Z23 Z24 Z25 Z26

Z31 Z31 Z32 Z33 Z34 Z35 Z36

Z41 Z41 Z42 Z43 Z44 Z45 Z46

Z51 Z51 Z52 Z53 Z54 Z55 Z56

Z11 minus Z13

Zi minus Zj

Z21 minus Z22

Z31 minus Z36

Z41 minus Z45

Z51 minus Z54

Figure 1 Differential mechanism illustrated

(4 6 45 12)

(3 5 50 11)(3 5 50 12)

(3 5 50 12)

(35

50

10

)(4

650

10

)

(33459)(1 4 45 11)

(8 12 50 25)

(6 6 45 10)

(4 6 45 12)

(345011)

(47 50 10)

(4 6 50 10)

(3 4 45 10)

(5 6 45 12)

(4 5 50 10) (5 7 45 8)(5 6 50 10)

(5 5 50 10)

(2 4 45 10)

(2 5 45 10)

(464511)

(4 5 45 11)

(4 2 50 10)

(57 50 12)

(125010)

(5 6 50 12)

(5 6 45 12)

(5 6 45 10)

(3 6 45 10)

(5 6 45 11)

(4 6 45 12)

(4 7 50 11)

(5 7 50 12)

(5 6 45 12)

(6 5 50 10)

(6 5 45 12) (5 7 45 12)

(5 6 45 11)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

Figure 2 Network used as test bench for Cases 1 and 2

executed for 30 trials on each case The performance ofthe proposed algorithm from the perspectives of the bestmulticast tree obtained best fitness value average fitnessvalue convergence speed and so forth is demonstrated

The multicast tree with the best fitness value of Cases 1and 2 that satisfies the constraints estimated out of 30 runs ofeach algorithm is shown in Figure 3The least cost delay anddelay-jitter of each identified multicast tree are summarizedin Table 1

In addition the mean and standard deviation of thebest fitness values in 30 trial runs of all algorithms underconsideration are also listedThe averaged values are obtainedfor delay and delay-jitter over all the paths of the multicasttree from the source node to the end nodes It is provedthat for both cases of the constraint sets the best fitnessvalue of the multicast trees generated by both QPSO [12]and proposed DGKH have the same least costs with the

considered constraints informing that DGKH algorithmcould guarantee better multicast tree than QPSO PSO andGA [12]

To demonstrate the convergence properties of the algo-rithms under considerations the convergence graph of bothKHA and DGKH algorithm on the problem is experi-mented and plotted Since this research did not implementother algorithms which are used for comparison the KHAand DGKH algorithms are considered Figure 3 traces thedynamic changes of cost average delay and average delay-jitter with the development of iteration for two algorithmsthat is QPSO [12] and the proposed DGKH algorithm Asevident from Figure 3 the convergence speed of DGHKis better It conveys that proposed DGKH algorithm hasstronger search ability than QPSO on the tested problem

To validate the proposed algorithm with additionalconstraints as mentioned in Case (3) the network under


0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

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20

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22

(a)

0

1

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3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

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22

(b)

Figure 3 Best multicast tree generated by DGKH algorithm constraint (a) Set 1 and (b) Set 2

Table 1 Summary of performance metrics by various methods for multiconstrained QoSR for various cases

Index Methods Best cost Average delay Average delay-jitter Average cost Standard deviation Average packet loss rate

Case 1 [12]

GA 138 185 302 14529 373 NAPSO 140 196 308 14383 359 NAQPSO 122 216 330 13520 325 NADGKH 122 221 333 12537 320 NA

Case 2 [12]


Case 3 KHA 135 218 322 13189 219 09442DGKH 127 213 324 12921 216 09370

(4 6 45 12 2)

(3 5 50 11 2)(3 5 50 12 4)

(355012 3)

(35

50

10

2)

(46

50

10

3)

(3 3 45 9 3) (144511 3)(8 12 50 25 4)

(6 6 45 10 3)

(4 6 45 12 2)

(3 4 50 11 3)(4 7 50 10 3)

(4 6 50 10 4)

(3 4 45 102)

(5 6 45 12 3)

(4 55010 4)

(5745 8 2)(5 6 50 10 2)

(5 5 50 102)

(2 4 45 10 3)

(2 5 45 10 2)

(4 6 45 11 4)

(4 5 45 11 3)

(4 2 50 10 4)

(575012 2)

(1 2 50 10 4)

(5 6 50 12 4)

(564512 3)

(5 6 45 104)

(3 6 45 193)

(5 6 45 11 2)

(4 6 45 12 2)

(4 7 50 11 2)

(5 7 50 12 3)

(5 6 45 12 3)

(6 5 50 10 4)

(654512 3) (574512 3)

(564511 4)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

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18

19

20

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Figure 4 Network used as test bench for Case 3


0

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5

6

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12

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(a)

0

1

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6

7

8

9

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12

13

14

15

16

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19

20

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22

(b)

Figure 5 Best multicast tree generated by DGKH algorithm constraint (a) Set 1 and (b) Set 2 for Case 3

Table 2 Network data

Parameter RangeCost of link 2ndash10Bandwidth 50ndash200 kbsDelay-jitter 5ndash15msBandwidth constraint 100ndash170Delay constraint 60ndash180Delay-jitter constraint 20ndash50

consideration is amended by including the packet loss rateconstraint in the last part of the representation Thus thefeatures of the edges in the proposed network as shown inFigure 4 are arranged by a pentuple (D DJ B C PL) withthe components representing delay delay-jitter band widthcost and packet loss respectivelyThemulticast tree as shownin Figure 5 with the best fitness value of Case 3 that satisfiesthe constraints estimated out of 30 runs of each algorithmis shown in Figure 5 The least cost delay delay-jitter andpacket loss of each identifiedmulticast tree for Case 3 are alsosummarized in Table 1

5 Experiments on Scalability

In this section numerical simulations were conducted inorder to investigate the scalability of the proposed DGKHalgorithm To achieve this objective we used the networktopologies created by Salama stochastic network topologygeneration [4 12] The data is adopted from [12] for compar-ison purpose and is shown in Table 2 Here the packet lossrate constraints are relaxed as the purpose of this section is todemonstrate the scalability of the proposedDGKHalgorithmfor QoSR The number of nodes of each network was setrandomly from 10 to 100 Table 3 summarizes the results ofthe proposed algorithm Due to the space limitation we onlyshow in Figure 6 the convergence properties of the algorithmsaveraged over 30 runs on the problem under constraint Set 2for Case 3

The other parameters of each algorithm were config-ured as in the first group of experiments The algorithms

25 50 75 100 125 150 175120

130

140

150

160

170

180

190

Number of iterations

DGKHKHA

Fitn

ess f

unct

ion

valu

e

Figure 6 Convergence plot for the KHA and DGKH algorithmwhile optimizing the fitness function

were evaluated from angles of least cost of obtained mul-ticast tree execution time and routing request successratio

By simulation scalability of the algorithm with the prob-lem size was evaluated according to execution time and leastcost of the obtained multicast tree For comparison purposethe plots of the proposed DGKH algorithm is merged withthe plots of the QPSO method We did not implement theQPSO at any part of this research The values of QPSO [12]are taken from the simulation software Figure 7 shows theleast cost generated by each algorithm that is averaged overdifferent constraints for the problems with different numbersof network nodes It can be observed that the multicasttree obtained by DGKH on each problem has best fitnessvalue compared to the QPSO method establishing it cangenerate the higher-quality solutions on themulticast routingproblems in MANETS Figure 8 shows the execution timeof the two algorithms in comparison to the problems withdifferent numbers of network nodes The results convey thesuperiority of the proposed method as the QPSO is moretime consuming than DGKH on the problems with the samenetwork scale In summary both the DGKH and the QPSO


Table 3 Performance metrics on the random networks of 10ndash100 nodes by the proposed DGKH algorithm

Nodes Best cost Average delay Average delay-jitter Average cost Standard deviation10 14825 213 342 14889 35220 30141 212 346 30263 42130 48036 212 342 48152 39640 56247 215 341 56331 45250 77523 214 339 77624 50160 92562 213 339 92622 36770 105231 213 345 105354 42380 121832 211 342 121889 38790 138495 211 341 138562 531100 157234 212 343 157305 654

10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160

Number of network nodes

Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO

Figure 7 The average cost in 30 runs of each algorithm on theproblems with different number of network nodes

algorithms for QoSR in MANETS seem to consume almostthe same amount of simulation time on the problem with thesame scale In conclusion when comparing two algorithmsfor OoS in multicast routing problem of MANETs DGKHmethod could generate best multicast trees (with best fitness(cost) values) compared to QPSO Additionally to find outthe solutions with same quality the DGKH algorithm hasconsumed (comparatively) least computational time amongits contestant algorithm QPSO

The performance of the algorithm can also be evaluatedby the routing request success ratio 120585req given by

120585req =119873ack119873req

(16)

where 119873ack is the number of successful routing requests and119873req is the number of all routing requests

Successful routing request means that the multicast treeobtained by the algorithm satisfies the bandwidth delay anddelay-jitter constraints [18] It is however too complicated tocompare all of the QoS parameters synchronouslyThereforethe performance is verified by each of QoS parameters Thecomparison of routing request success ratios among DGKH

DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)

Figure 8 The execution time of each algorithm on the problemswith different number of network nodes

and QPSO is curved and shown in Figure 9 It is proved thatDGKH has the highest success ratio according to each QoSparameter and thus has the best convergence performance

6 Conclusion

A QoS multicast routing method based on a modified krillherd algorithm is proposed in this paper Searching for thefeasibleoptimal route after simultaneously satisfying morethan oneQoS constraint inwirelessmobile ad hoc networks isclassified as an NP-complete problem This research consid-ers four different constraints while optimizing the total costof the multicast tree Hence the original krill herd algorithmis refined to perform the thorough exploration of the searchspace by differentially guided mechanism to update theirkrill individual positions Experimental result reveals theproposed thatDGKHalgorithm can search the solution spacein a very effective and efficient manner Simulation resultsalso shows that the proposed algorithm can search the bettermulticast trees with rapider convergence speed effectivelycompared with other algorithms


60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(c)Figure 9 Comparisons of routing request success ratio (a) Delay (b) bandwidth and (c) delay-jitter

As a future work we plan to consider other heuristictechniques for estimation of multicast routing consideringother constraints like queuing delays propagation errormaximum link utilization bandwidth consumption param-eters blocking probability and so forth as multiobjectiveoptimization problem

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] V P Kompella J C Pasquale and G C Polyzos ldquoMulticastrouting for multimedia communicationrdquo IEEEACM Transac-tions on Networking vol 1 no 3 pp 286ndash292 1993

[2] W-L Yang ldquoOptimal and heuristic algorithms for quality-of-service routing with multiple constraintsrdquo Performance Evalua-tion vol 57 no 3 pp 261ndash278 2004

[3] L Junhai X Liu and Y Danxia ldquoResearch onmulticast routingprotocols formobile ad-hoc networksrdquoComputerNetworks vol52 no 5 pp 988ndash997 2008

[4] H F Salama Y Director-Viniotis and D S Director-ReevesMulticast Routing for Real-Time Communication of High-SpeedNetworks North Carolina State University Raleigh NC USA1996

[5] K Kunavut and T Sanguankotchakorn ldquoMulti-ConstrainedPath (MCP) QoS routing in OLSR based on multiple additiveQoS metricsrdquo in Proceedings of the International Symposium onCommunications and Information Technologies (ISCIT rsquo10) pp226ndash231 IEEE October 2010

[6] L Liu and G Feng ldquoSimulated annealing based multi-cons-trained QoS routing in mobile ad hoc networksrdquo WirelessPersonal Communications vol 41 no 3 pp 393ndash405 2007

[7] C Lin and C Chuang ldquoA rough penalty genetic algorithm formulticast routing inmobile ad hoc networksrdquo Journal of AppliedMathematics vol 2013 Article ID 986985 11 pages 2013

[8] F Xiang L Junzhou W Jieyi and G Guanqun ldquoQoS routingbased on genetic algorithmrdquo Computer Communications vol22 no 15 pp 1392ndash1399 1999

[9] C Li C Cao Y Li and Y Yu ldquoHybrid of genetic algorithmand particle swarm optimization for multicast QoS routingrdquo inProceedings of the IEEE International Conference on Control andAutomation (ICCA rsquo07) pp 2355ndash2359 IEEE June 2007


[10] D Ruperez Canas A L Sandoval Orozco L J Garcıa Villalbaand P-S Hong ldquoHybrid ACO routing protocol for mobileAd Hoc networksrdquo International Journal of Distributed SensorNetworks vol 2013 Article ID 265485 7 pages 2013

[11] H Wang H Xu S Yi and Z Shi ldquoA tree-growth based antcolony algorithm for QoS multicast routing problemrdquo ExpertSystems with Applications vol 38 no 9 pp 11787ndash11795 2011

[12] J Sun W Fang X Wu Z Xie and W Xu ldquoQoS multicastrouting using a quantum-behaved particle swarm optimizationalgorithmrdquo Engineering Applications of Artificial Intelligencevol 24 no 1 pp 123ndash131 2011

[13] H Wang X Meng S Li and H Xu ldquoA tree-based particleswarm optimization formulticast routingrdquoComputer Networksvol 54 no 15 pp 2775ndash2786 2010

[14] S Bitam and A Mellouk ldquoBee life-based multi constraintsmulticast routing optimization for vehicular ad hoc networksrdquoJournal of Network and Computer Applications vol 36 no 3 pp981ndash991 2013

[15] N Ghaboosi and A T Haghighat ldquoTabu search based algo-rithms for bandwidth-delay-constrained least-cost multicastroutingrdquo Telecommunication Systems vol 34 no 3-4 pp 147ndash166 2007

[16] R Forsati A T Haghighat and M Mahdavi ldquoHarmony searchbased algorithms for bandwidth-delay-constrained least-costmulticast routingrdquo Computer Communications vol 31 no 10pp 2505ndash2519 2008

[17] A H Gandomi and A H Alavi ldquoKrill herd a new bio-inspiredoptimization algorithmrdquo Communications in Nonlinear Scienceand Numerical Simulation vol 17 no 12 pp 4831ndash4845 2012

[18] L Zhang L-B Cai M Li and F-H Wang ldquoA method forleast-cost QoS multicast routing based on genetic simulatedannealing algorithmrdquo Computer Communications vol 32 no1 pp 105ndash110 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


for solving optimization (GO) problems of NP nature antcolony optimization (ACO) and particle swarmoptimization(PSO) is introduced

Similar to GA these two methods were also shown tobe efficient tools for solving the multicast routing problem[10ndash13] In [10 11] theQoS-multiple constrained optimizationproblem has been solved using ant colony optimization(ACO) algorithm Here the authors examined the degree anddelay-constrained broadcasting problem with minimum costusing an ant colony-based algorithm After simulations andcomparisons with previous ant algorithm and to two GA-based algorithms the obtained results exhibited the best costbut again with too long computation time

Consequently PSO [12 13] was also used to addressthe QoSR problem PSO can be easily implemented andis computationally inexpensive since its memory and CPUspeed requirements are low PSO has been proved to be anefficient approach for many optimization problems with itsfast convergence and simple steps to solve a problem In spiteof these merits a known fact that PSO has a severe drawbackin the update of its global best (gbest) particle which has acrucial role of guiding the rest of the particles this leads toovercoming better solutions in the course of search

In row of these heuristics another new metaheuristiccalled Bees Life Algorithm (BLA) is proposed [14] As oneof the specie colony optimization BLA is considered asa swarm intelligence algorithm and an approximate opti-mization method which performs according to collaborativeindividual behaviors in the population But still like otherprobabilistic optimization algorithms BLA has inherentdrawback of premature convergence or stagnation that leadsto loss of exploration and exploitation capability In line tothis other heuristics like tabu search [15] and harmony searchalgorithm [16] were proposed for QoSR with minimumnumber of constraints

In fact there is a growing body of literature in theapplication of emerging heuristics to solve theNP-hardQoSRproblemThis paper proposes a krill herd based algorithm forQoSR in MANETS Krill herd algorithm (KHA) is a recentlydeveloped powerful evolutionary algorithm proposed byGandomi and Alavi [17] The KHA is based on the herdingbehavior of krill individuals Each krill individual modifiesits position using three processes namely (1) movementinduced by other individuals (2) foraging motion and (3)

random physical diffusion The motion induced by otherindividuals and foraging motion contain global and localstrategies respectively which make KHA a powerful tech-niqueHowever sometimes KHA is unable to generate globaloptimal solutions on some high-dimensional nonlinear opti-mization problems

Thus this paper proposes a differentially guided krillherd (DGKH) algorithm where the krill individuals do notupdate the position in comparisonwith one-to-one (as usual)instead it uses the information from various krill individualsand then searches to determine a feasible path Thus theinduction stage uses the position information from variouskrill individuals at random making the search exhaustiveand leads to quick search of better solutions

The rest of the paper is organized as follows In Section 2the problem statement of QoS routing problem in MANETSis introduced The overview of KHA is briefly explainedin Section 3 with description of the proposed differentialguiding mechanism Section 4 presents the numerical exper-iments with a standard QoS multicast routing problem Adetailed discussion about the proposedmethod in theoreticalperspective is detailed in Section 5The paper is concluded inSection 6

2 Problem Statement

Let 119866 = (119881 119864) be an undirected graph representing thenetwork topology where 119881 is the set of nodes and 119864 is theset of links The source node and the multicast destinationnode set containing 119903 destinations are the routes for multicast[18] The end-to-end QoS requirements are expressed asconstraints from the source to the destinations and are givenby the following

The delay (DL) is themaximumdelay along any branch of thetree A penalty is added if no link is found between two nodesConsider

119863 (119901 (119904 119905)) = sum119890isin119901(119904119905)

delay (119890) + sum119899isin119901(119904119905)

delay (119899) (1)

The bandwidth (BW) of the multicast tree is the averagebandwidth requirement of all the tree branches Consider

119861 (119901 (119904 119905)) = min (bandwidth (119890)) 119890 isin 119901 (119904 119905) (2)

The delay-jitter (DJ) is the maximum delay variation alongany branch of the tree Consider

DJ (119901 (119904 119905)) = sum119890isin119901(119904119905)

delay jitter (119890) + sum119899isin119901(119904119905)

delay jitter (119899)

(3)

The packet loss rate is the average packet loss along the treebranchesThe cutoff for PLR is set at 10 If a branch is havingmore than 10 packet loss then a penalty is assigned suchthat the model tries to search a path less than 10 PLR

PL (119901 (119904 119905)) = 1 minus prod119899isin119901(119904119905)

(1 minus packet loss (119899)) (4)

The above QoS criteria have to be fulfilled with an objectiveto minimize cost function of the multicast tree as given by

119862 (119879 (119904 119872)) = sum119890isin119879(119904119872)

cos 119905 (119890) + sum119899isin119879(119904119872)

cos 119905 (119899) (5)

Thus the QoS routing problem is formulated as an optimiza-tion problem whose goal is to find a multicast tree 119879(119904 119872)



Minimize 119862 (119879 (119904 119872))

st D (119901 (119904 119879)) le QD

B (119901 (119904 119879)) ge QB

DJ (119901 (119904 119879)) le QDJ

PL (119901 (119904 119879)) le QPL

(6)


Minimize 119891 (119879 (119904 119872))

= 119891119888

+ 1205961119891119887

+ 1205962119891119889

+ 1205963119891dj + 120596

4119891pl

(7)

where119891119888

= cos 119905 (119879 (119904 119872))

119891119887

= sum119905isin119872

max QB minus B (119901 (119904 119905)) 0

119891119889

= sum119905isin119872

max D (119901 (119904 119905)) minus QD 0

119891dj = sum119905isin119872

max DJ (119901 (119904 119905)) minus QJ 0

119891pl = sum119905isin119872

max PL (119901 (119904 119905)) minus QPL 0

(8)








V119898119894

= 120572119894Vmax119894

+ 120596119899V119898minus1119894

(9)

120572119894=

119873119878

sum119895=1

[119891119894minus 119891119895

119891119908

minus 119891119887

times119885119894minus 119885119895

10038161003816100381610038161003816119885119894minus 119885119895

10038161003816100381610038161003816+ rand (0 1)

]

+ 2 [rand (0 1) +119894

119894max] 119891

best119894

119885best119894

(10)

where 119881max119894


and 119881119898minus1119894



119891119908and 119891






SD119894=

1

5119899119901

119899119901

sum119896=1

1003816100381610038161003816119885119894 minus 119885119896

1003816100381610038161003816 (11)


119894and 119885




119881119898

119891119894

= 002 [2 (1 minus119894

119894max) 119891119894

sum119873119878

119896=1(119885119896119891119896)

sum119873119878

119896=1(1119891119896)

+ 119891best119894

119883best119894

]

+ 120596119909119881119898minus1

119891119894

(12)


119891119894

and119881119898119891119894



V119898119863119894

= 120583Vmax119863

(13)





119885119898+1

119894= 119885119898

119894+ (119881119898

119894+ 119881119898

119891119894

+ 119881119898

119863119894

) 119875119905

119873119889

sum119895=1

(119906119895

minus 119897119895) (14)


119895and 119897119895are the











119885119894minus 119885119895

= (1199111198941

1199111198942

1199111198943

sdot sdot sdot 119911119894119899

) minus (1199111205881

1199111205882

1199111205883

sdot sdot sdot 119911120588119899

)

(15)


119894 119911119894119899











Dim

ensio

n

Z11 Z11 Z12 Z13 Z14 Z15 Z16

Z21 Z21 Z22 Z23 Z24 Z25 Z26

Z31 Z31 Z32 Z33 Z34 Z35 Z36

Z41 Z41 Z42 Z43 Z44 Z45 Z46

Z51 Z51 Z52 Z53 Z54 Z55 Z56

Z11 minus Z13

Zi minus Zj

Z21 minus Z22

Z31 minus Z36

Z41 minus Z45

Z51 minus Z54


(4 6 45 12)

(3 5 50 11)(3 5 50 12)

(3 5 50 12)

(35

50

10

)(4

650

10

)

(33459)(1 4 45 11)

(8 12 50 25)

(6 6 45 10)

(4 6 45 12)

(345011)

(47 50 10)

(4 6 50 10)

(3 4 45 10)

(5 6 45 12)

(4 5 50 10) (5 7 45 8)(5 6 50 10)

(5 5 50 10)

(2 4 45 10)

(2 5 45 10)

(464511)

(4 5 45 11)

(4 2 50 10)

(57 50 12)

(125010)

(5 6 50 12)

(5 6 45 12)

(5 6 45 10)

(3 6 45 10)

(5 6 45 11)

(4 6 45 12)

(4 7 50 11)

(5 7 50 12)

(5 6 45 12)

(6 5 50 10)

(6 5 45 12) (5 7 45 12)

(5 6 45 11)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22









0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)




Case 1 [12]


Case 2 [12]


Case 3 KHA 135 218 322 13189 219 09442DGKH 127 213 324 12921 216 09370

(4 6 45 12 2)

(3 5 50 11 2)(3 5 50 12 4)

(355012 3)

(35

50

10

2)

(46

50

10

3)

(3 3 45 9 3) (144511 3)(8 12 50 25 4)

(6 6 45 10 3)

(4 6 45 12 2)

(3 4 50 11 3)(4 7 50 10 3)

(4 6 50 10 4)

(3 4 45 102)

(5 6 45 12 3)

(4 55010 4)

(5745 8 2)(5 6 50 10 2)

(5 5 50 102)

(2 4 45 10 3)

(2 5 45 10 2)

(4 6 45 11 4)

(4 5 45 11 3)

(4 2 50 10 4)

(575012 2)

(1 2 50 10 4)

(5 6 50 12 4)

(564512 3)

(5 6 45 104)

(3 6 45 193)

(5 6 45 11 2)

(4 6 45 12 2)

(4 7 50 11 2)

(5 7 50 12 3)

(5 6 45 12 3)

(6 5 50 10 4)

(654512 3) (574512 3)

(564511 4)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22



0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)








25 50 75 100 125 150 175120

130

140

150

160

170

180

190


DGKHKHA

Fitn

ess f

unct

ion

valu

e







10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160


Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO




120585req =119873ack119873req

(16)



DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)



6 Conclusion



60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Minimize 119862 (119879 (119904 119872))

st D (119901 (119904 119879)) le QD

B (119901 (119904 119879)) ge QB

DJ (119901 (119904 119879)) le QDJ

PL (119901 (119904 119879)) le QPL

(6)


Minimize 119891 (119879 (119904 119872))

= 119891119888

+ 1205961119891119887

+ 1205962119891119889

+ 1205963119891dj + 120596

4119891pl

(7)

where119891119888

= cos 119905 (119879 (119904 119872))

119891119887

= sum119905isin119872

max QB minus B (119901 (119904 119905)) 0

119891119889

= sum119905isin119872

max D (119901 (119904 119905)) minus QD 0

119891dj = sum119905isin119872

max DJ (119901 (119904 119905)) minus QJ 0

119891pl = sum119905isin119872

max PL (119901 (119904 119905)) minus QPL 0

(8)








V119898119894

= 120572119894Vmax119894

+ 120596119899V119898minus1119894

(9)

120572119894=

119873119878

sum119895=1

[119891119894minus 119891119895

119891119908

minus 119891119887

times119885119894minus 119885119895

10038161003816100381610038161003816119885119894minus 119885119895

10038161003816100381610038161003816+ rand (0 1)

]

+ 2 [rand (0 1) +119894

119894max] 119891

best119894

119885best119894

(10)

where 119881max119894


and 119881119898minus1119894



119891119908and 119891






SD119894=

1

5119899119901

119899119901

sum119896=1

1003816100381610038161003816119885119894 minus 119885119896

1003816100381610038161003816 (11)


119894and 119885




119881119898

119891119894

= 002 [2 (1 minus119894

119894max) 119891119894

sum119873119878

119896=1(119885119896119891119896)

sum119873119878

119896=1(1119891119896)

+ 119891best119894

119883best119894

]

+ 120596119909119881119898minus1

119891119894

(12)


119891119894

and119881119898119891119894



V119898119863119894

= 120583Vmax119863

(13)





119885119898+1

119894= 119885119898

119894+ (119881119898

119894+ 119881119898

119891119894

+ 119881119898

119863119894

) 119875119905

119873119889

sum119895=1

(119906119895

minus 119897119895) (14)


119895and 119897119895are the











119885119894minus 119885119895

= (1199111198941

1199111198942

1199111198943

sdot sdot sdot 119911119894119899

) minus (1199111205881

1199111205882

1199111205883

sdot sdot sdot 119911120588119899

)

(15)


119894 119911119894119899











Dim

ensio

n

Z11 Z11 Z12 Z13 Z14 Z15 Z16

Z21 Z21 Z22 Z23 Z24 Z25 Z26

Z31 Z31 Z32 Z33 Z34 Z35 Z36

Z41 Z41 Z42 Z43 Z44 Z45 Z46

Z51 Z51 Z52 Z53 Z54 Z55 Z56

Z11 minus Z13

Zi minus Zj

Z21 minus Z22

Z31 minus Z36

Z41 minus Z45

Z51 minus Z54


(4 6 45 12)

(3 5 50 11)(3 5 50 12)

(3 5 50 12)

(35

50

10

)(4

650

10

)

(33459)(1 4 45 11)

(8 12 50 25)

(6 6 45 10)

(4 6 45 12)

(345011)

(47 50 10)

(4 6 50 10)

(3 4 45 10)

(5 6 45 12)

(4 5 50 10) (5 7 45 8)(5 6 50 10)

(5 5 50 10)

(2 4 45 10)

(2 5 45 10)

(464511)

(4 5 45 11)

(4 2 50 10)

(57 50 12)

(125010)

(5 6 50 12)

(5 6 45 12)

(5 6 45 10)

(3 6 45 10)

(5 6 45 11)

(4 6 45 12)

(4 7 50 11)

(5 7 50 12)

(5 6 45 12)

(6 5 50 10)

(6 5 45 12) (5 7 45 12)

(5 6 45 11)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22









0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)




Case 1 [12]


Case 2 [12]


Case 3 KHA 135 218 322 13189 219 09442DGKH 127 213 324 12921 216 09370

(4 6 45 12 2)

(3 5 50 11 2)(3 5 50 12 4)

(355012 3)

(35

50

10

2)

(46

50

10

3)

(3 3 45 9 3) (144511 3)(8 12 50 25 4)

(6 6 45 10 3)

(4 6 45 12 2)

(3 4 50 11 3)(4 7 50 10 3)

(4 6 50 10 4)

(3 4 45 102)

(5 6 45 12 3)

(4 55010 4)

(5745 8 2)(5 6 50 10 2)

(5 5 50 102)

(2 4 45 10 3)

(2 5 45 10 2)

(4 6 45 11 4)

(4 5 45 11 3)

(4 2 50 10 4)

(575012 2)

(1 2 50 10 4)

(5 6 50 12 4)

(564512 3)

(5 6 45 104)

(3 6 45 193)

(5 6 45 11 2)

(4 6 45 12 2)

(4 7 50 11 2)

(5 7 50 12 3)

(5 6 45 12 3)

(6 5 50 10 4)

(654512 3) (574512 3)

(564511 4)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22



0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)








25 50 75 100 125 150 175120

130

140

150

160

170

180

190


DGKHKHA

Fitn

ess f

unct

ion

valu

e







10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160


Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO




120585req =119873ack119873req

(16)



DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)



6 Conclusion



60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119885119898+1

119894= 119885119898

119894+ (119881119898

119894+ 119881119898

119891119894

+ 119881119898

119863119894

) 119875119905

119873119889

sum119895=1

(119906119895

minus 119897119895) (14)


119895and 119897119895are the











119885119894minus 119885119895

= (1199111198941

1199111198942

1199111198943

sdot sdot sdot 119911119894119899

) minus (1199111205881

1199111205882

1199111205883

sdot sdot sdot 119911120588119899

)

(15)


119894 119911119894119899











Dim

ensio

n

Z11 Z11 Z12 Z13 Z14 Z15 Z16

Z21 Z21 Z22 Z23 Z24 Z25 Z26

Z31 Z31 Z32 Z33 Z34 Z35 Z36

Z41 Z41 Z42 Z43 Z44 Z45 Z46

Z51 Z51 Z52 Z53 Z54 Z55 Z56

Z11 minus Z13

Zi minus Zj

Z21 minus Z22

Z31 minus Z36

Z41 minus Z45

Z51 minus Z54


(4 6 45 12)

(3 5 50 11)(3 5 50 12)

(3 5 50 12)

(35

50

10

)(4

650

10

)

(33459)(1 4 45 11)

(8 12 50 25)

(6 6 45 10)

(4 6 45 12)

(345011)

(47 50 10)

(4 6 50 10)

(3 4 45 10)

(5 6 45 12)

(4 5 50 10) (5 7 45 8)(5 6 50 10)

(5 5 50 10)

(2 4 45 10)

(2 5 45 10)

(464511)

(4 5 45 11)

(4 2 50 10)

(57 50 12)

(125010)

(5 6 50 12)

(5 6 45 12)

(5 6 45 10)

(3 6 45 10)

(5 6 45 11)

(4 6 45 12)

(4 7 50 11)

(5 7 50 12)

(5 6 45 12)

(6 5 50 10)

(6 5 45 12) (5 7 45 12)

(5 6 45 11)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22









0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)




Case 1 [12]


Case 2 [12]


Case 3 KHA 135 218 322 13189 219 09442DGKH 127 213 324 12921 216 09370

(4 6 45 12 2)

(3 5 50 11 2)(3 5 50 12 4)

(355012 3)

(35

50

10

2)

(46

50

10

3)

(3 3 45 9 3) (144511 3)(8 12 50 25 4)

(6 6 45 10 3)

(4 6 45 12 2)

(3 4 50 11 3)(4 7 50 10 3)

(4 6 50 10 4)

(3 4 45 102)

(5 6 45 12 3)

(4 55010 4)

(5745 8 2)(5 6 50 10 2)

(5 5 50 102)

(2 4 45 10 3)

(2 5 45 10 2)

(4 6 45 11 4)

(4 5 45 11 3)

(4 2 50 10 4)

(575012 2)

(1 2 50 10 4)

(5 6 50 12 4)

(564512 3)

(5 6 45 104)

(3 6 45 193)

(5 6 45 11 2)

(4 6 45 12 2)

(4 7 50 11 2)

(5 7 50 12 3)

(5 6 45 12 3)

(6 5 50 10 4)

(654512 3) (574512 3)

(564511 4)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22



0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)








25 50 75 100 125 150 175120

130

140

150

160

170

180

190


DGKHKHA

Fitn

ess f

unct

ion

valu

e







10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160


Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO




120585req =119873ack119873req

(16)



DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)



6 Conclusion



60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Dim

ensio

n

Z11 Z11 Z12 Z13 Z14 Z15 Z16

Z21 Z21 Z22 Z23 Z24 Z25 Z26

Z31 Z31 Z32 Z33 Z34 Z35 Z36

Z41 Z41 Z42 Z43 Z44 Z45 Z46

Z51 Z51 Z52 Z53 Z54 Z55 Z56

Z11 minus Z13

Zi minus Zj

Z21 minus Z22

Z31 minus Z36

Z41 minus Z45

Z51 minus Z54


(4 6 45 12)

(3 5 50 11)(3 5 50 12)

(3 5 50 12)

(35

50

10

)(4

650

10

)

(33459)(1 4 45 11)

(8 12 50 25)

(6 6 45 10)

(4 6 45 12)

(345011)

(47 50 10)

(4 6 50 10)

(3 4 45 10)

(5 6 45 12)

(4 5 50 10) (5 7 45 8)(5 6 50 10)

(5 5 50 10)

(2 4 45 10)

(2 5 45 10)

(464511)

(4 5 45 11)

(4 2 50 10)

(57 50 12)

(125010)

(5 6 50 12)

(5 6 45 12)

(5 6 45 10)

(3 6 45 10)

(5 6 45 11)

(4 6 45 12)

(4 7 50 11)

(5 7 50 12)

(5 6 45 12)

(6 5 50 10)

(6 5 45 12) (5 7 45 12)

(5 6 45 11)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22









0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)




Case 1 [12]


Case 2 [12]


Case 3 KHA 135 218 322 13189 219 09442DGKH 127 213 324 12921 216 09370

(4 6 45 12 2)

(3 5 50 11 2)(3 5 50 12 4)

(355012 3)

(35

50

10

2)

(46

50

10

3)

(3 3 45 9 3) (144511 3)(8 12 50 25 4)

(6 6 45 10 3)

(4 6 45 12 2)

(3 4 50 11 3)(4 7 50 10 3)

(4 6 50 10 4)

(3 4 45 102)

(5 6 45 12 3)

(4 55010 4)

(5745 8 2)(5 6 50 10 2)

(5 5 50 102)

(2 4 45 10 3)

(2 5 45 10 2)

(4 6 45 11 4)

(4 5 45 11 3)

(4 2 50 10 4)

(575012 2)

(1 2 50 10 4)

(5 6 50 12 4)

(564512 3)

(5 6 45 104)

(3 6 45 193)

(5 6 45 11 2)

(4 6 45 12 2)

(4 7 50 11 2)

(5 7 50 12 3)

(5 6 45 12 3)

(6 5 50 10 4)

(654512 3) (574512 3)

(564511 4)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22



0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)








25 50 75 100 125 150 175120

130

140

150

160

170

180

190


DGKHKHA

Fitn

ess f

unct

ion

valu

e







10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160


Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO




120585req =119873ack119873req

(16)



DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)



6 Conclusion



60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)




Case 1 [12]


Case 2 [12]


Case 3 KHA 135 218 322 13189 219 09442DGKH 127 213 324 12921 216 09370

(4 6 45 12 2)

(3 5 50 11 2)(3 5 50 12 4)

(355012 3)

(35

50

10

2)

(46

50

10

3)

(3 3 45 9 3) (144511 3)(8 12 50 25 4)

(6 6 45 10 3)

(4 6 45 12 2)

(3 4 50 11 3)(4 7 50 10 3)

(4 6 50 10 4)

(3 4 45 102)

(5 6 45 12 3)

(4 55010 4)

(5745 8 2)(5 6 50 10 2)

(5 5 50 102)

(2 4 45 10 3)

(2 5 45 10 2)

(4 6 45 11 4)

(4 5 45 11 3)

(4 2 50 10 4)

(575012 2)

(1 2 50 10 4)

(5 6 50 12 4)

(564512 3)

(5 6 45 104)

(3 6 45 193)

(5 6 45 11 2)

(4 6 45 12 2)

(4 7 50 11 2)

(5 7 50 12 3)

(5 6 45 12 3)

(6 5 50 10 4)

(654512 3) (574512 3)

(564511 4)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22



0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)








25 50 75 100 125 150 175120

130

140

150

160

170

180

190


DGKHKHA

Fitn

ess f

unct

ion

valu

e







10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160


Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO




120585req =119873ack119873req

(16)



DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)



6 Conclusion



60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(a)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

(b)








25 50 75 100 125 150 175120

130

140

150

160

170

180

190


DGKHKHA

Fitn

ess f

unct

ion

valu

e







10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160


Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO




120585req =119873ack119873req

(16)



DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)



6 Conclusion



60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












10 20 30 40 50 60 70 80 90 100

40

60

80

100

120

140

160


Leas

t cos

t of

mul

ticas

t tre

es

DGKHQPSO




120585req =119873ack119873req

(16)



DGKHQPSO

10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8


Exec

utio

n tim

e (s

)



6 Conclusion



60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










60 80 100 120 140 160 18001

02

03

04

05

06

07

08

09

1

Delay (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(a)

100 110 120 130 140 150 160 17002

04

06

08

1

12

Bandwidth (kbs)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH

(b)

20 25 30 35 40 45 500

02

04

06

08

1

Delay-jitter (ms)

Rout

ing

requ

est s

ucce

ss ra

tio

QPSODGKH





References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article multiconstrained qos routing using a...

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