Research ArticleHybrid Wireless Sensor Network CoverageHoles Restoring Algorithm
Liu Zhouzhou and Yanhong She
Xirsquoan Aeronautical University Xirsquoan 710077 China
Correspondence should be addressed to Liu Zhouzhou liuzhouzhou8192126com
Received 25 November 2015 Revised 6 April 2016 Accepted 27 April 2016
Academic Editor Fanli Meng
Copyright copy 2016 L Zhouzhou and Y She This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Aiming at the perception hole caused by the necessary movement or failure of nodes in the wireless sensor actuator networkthis paper proposed a kind of coverage restoring scheme based on hybrid particle swarm optimization algorithm The schemefirst introduced network coverage based on grids transformed the coverage restoring problem into unconstrained optimizationproblem taking the network coverage as the optimization target and then solved the optimization problem in the use of the hybridparticle swarm optimization algorithmwith the idea of simulated annealing Simulation results show that the probabilistic jumpingproperty of simulated annealing algorithm could make up for the defect that particle swarm optimization algorithm is easy to fallinto premature convergence and the hybrid algorithm can effectively solve the coverage restoring problem
1 Introduction
Wireless Sensor and Actuator Network WSAN is an ad hocand multihop network system which is composed of a largequantity of microsensor nodes laid in unattended monitor-ing areas and formed by wireless communication methodThe purpose of the system is to provide detailed and accurateinformation to remote observer by cooperatively sensingconnecting and dealing with perceived object informationin monitoring areas and then processing them [1] Since thesensor nodes are with some real constraints nodes energy islimited moreover it is unrealistic to supplement energy byreplacing battery nodes communication capability is limitedand so forth so network coverage research can be taken asto optimize allocation of various limited resources withinsensor network through node deployment and node positionadjustment hence to effectively improve various servicesquality environmental perception information acquisitiondata transmission and network survival ability and so forth
Moreover after the network running for some time dueto some nodes energy depletion or physical damage and soforth network awareness and communication capabilities arereduced which results in coverage hole thereby affectingnetwork coverage Coverage hole will cause perceptual
information incompletion reduce information validity andmake network communication not smooth thus affectingwhole network performance To fulfill related task and realizeits value firstly wireless sensor actuator network must covermonitoring areas well Network coverage is an importantindicator to judge wireless sensor actuator network perfor-mance and service quality
Currently coverage restoring unconstrained optimiza-tion has two categories wherein one is to add nodes innetwork hole and another is to move existing nodes WangandWu [2] propose a distributed hole detection and restoringmethod under trap coverage wherein hole detection methodenables node to confirm hole position autonomously thenby adding nodes in hole network coverage increases Lunet al [3] use particle swarm optimization algorithm to findsink node position in randomly arranged network and thenincrease network coverage and optimize topology of networkAiming at coverage restoring problem in dense distributedwireless sensor network Yang et al [4] propose coveragerestoring algorithm SOI which calculates nodes movingdirection and best position to move on hole edge and thenexpandnodes coverage by nodesmoving hence fulfilling net-work coverage restoring Lee et al [5] propose CRAFT withcertain fault tolerance to solve network coverage problem
Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 8064509 9 pageshttpdxdoiorg10115520168064509
2 Journal of Sensors
which establishes two-way connection zoning topologybuilds the largest backbone around damaged area center andthen deploys the relay nodes (RNs) to connect each partitionto the backbone outer polygon Simulation states that thisalgorithm can get topology with high coverage by placingless relay nodes With distributed self-deployment strategySenturk et al [6] recover continuity of zone wireless sensornetwork and proposes two methods to locate relay nodeswherein the first one is based onmovement of relay nodes vir-tual force and the second one is based on game theory in zoneguiding nodes Simulation states that in most situations themethod based on game theory performs better than the oneon virtual force Aiming at the coverage decrease problemdueto the failure of many nodes in network Zhao and Wang [7]propose a flow-based multiobjective nonlinear mathematicalprogramming model which decreases coverage by movingnodes in network takes the total travel distance of nodes andsingle travel distance as optimization target and then usesflow equilibrium conditions to restore network coverage
As current improvement on integrated circuit technologyleads to lower energy consumption on sensor and processorrelatively the communication energy consumption betweennodes becomes too low to consider So when calculating theenergy consumption the communication energy consump-tion can be ignored Move energy consumption is defined asthe energy consumed when attack node moves towards bestattack point so move energy consumption is proportional tothe distance that attack nodes moves in hence distance thatattack nodes moves in can be used to calculate move energyconsumption directly
2 Models for Problem Solving
21 Node Sensing Model Node Sensing Model [8 9] isa prior problem in network coverage control technologyThree main perception models have been used in recentresearch work which include Circumference Sensing ModelProbability Sensing Model and Direction Sensing ModelCircumference SensingModel defines nodes sensing range asa round enclosed area which takes nodes location as centerand sensing radius 119877
119904as radius The sensing radius 119877
119904is
decided by physical characteristics of the sensor Any pointin this round area can be sensed by node
Circumference Sensing Model assumes that uncertaintydoes not exist when the sensor senses target area But inpractical application due to the disruptive factors such asambient noise obstacle and the feature that wireless signalintensity decays along with the communication distanceincrease circumference Sensing Model cannot reflect nodessensing feature well Probability Sensing Model considersthe uncertainty of node sensing in practical applicationwherein the probability that an intruder 119889 sensed by node 119899is expressed as119901119904(119899 119889)
=
1 119877119904minus 119903 ge
1003817100381710038171003817(119909119899 119910119899) minus (119909119889 119910119889)1003817100381710038171003817
119890minus120582sdot120572120573
119877119904minus 119903 le
1003817100381710038171003817(119909119899 119910119899) minus (119909119889 119910119889)1003817100381710038171003817 le 119877119904+ 119903
0 119877119904+ 119903 le
1003817100381710038171003817(119909119899 119910119899) minus (119909119889 119910119889)1003817100381710038171003817
(1)
Determineperceived area
Uncertaintyperception area
R s+r
Rsrr
Rsminusr
Figure 1 Probability Sensing Model
In this formula 119877119904is for the max sensed radius without
disruptive factors 119903 is for measuring nodes uncertain moni-toring ability Arguments 120572 = (119909
119899 119910119899) minus (119909
119889 119910119889) minus (119877
119904minus 119903)
wherein 120582 and 120573 are for intruder sensed probability value bynode when intruder is in uncertainmonitoring area Physicalcharacteristic of Probability Sensing Model is as shown inFigure 1
Sensing direction of the two Sensing Models is omni-direction But in practical application some sensors havecertain direction wherein only when intruder is in certaindirection of nodes can they be sensed The Node SensingModel setup under this feature is called Directed SendingModel
22 Related Definitions
Definition 1 (effective coverage area) Supposing an intrudercan be sensed by node at any point in designated area thenthe designated area is called coverage area 120595(119894) of node 119894Effective coverage area 119894 is defined as intersection of coveragearea 120595(119894) and monitor areaΩ
120585 (119894) = 120595 (119894) cap Ω (2)
Definition 2 (coverage ratio) Coverage ratio of node 119894 isdefined as the area ratio of effective node coverage area 120585(119894)to monitor area Ω Network coverage ratio is defined as thearea ratio of the union of all node effective coverage areasin monitor area Network coverage ratio is an importantindicator of the quality of network coverage
120578 =119878 (⋃119894120585 (119894))
119878 (Ω) (3)
Definition 3 (connectivity) If two nodes can communicatethrough single-hop or multi-hop network then they arecalled connected Supposing that the total number of nodes inmonitor area is 119899 obviously the nodes number 120577(119894) connected
Journal of Sensors 3
O4 O1
O3
O2
Figure 2 The multioverlapping of coverage region
with node 119894 will satisfy the formula 0 le 120577(119894) le 119899 minus 1 If allnodes can communicate between each other then the totalnumber of communication paths is 119899(119899 minus 1)2 Connectivityof network is defined as the total number ratio of currentcommunication path to max communication path
120591 =12 sdot sum
119894120577 (119894)
119899 (119899 minus 1) 2=
sum119894120577 (119894)
119899 (119899 minus 1) (4)
When doing research on network coverage problem thepaper supposes that network and nodes have the followingcharacteristics
(1) Nodes in network are isomorphic and movable andhave unique short addresses to identify themselves
(2) Sensing model of nodes is Probability SensingModelwhich has the same sensing radius 119877
119904and communi-
cation radius 119877119888 andmeets 119877
119888ge 2 sdot119877
119904 When it meets
this condition network coverage problem is of equalvalue to connection problem
Monitor area is a square area with side length 119871and 119873 nodes are randomly and evenly deployed inmonitor area
(3) Each node gets its own location information fromself-positioning of network and then broadcasts to theentire network
23 Network Coverage Based on Grids Ideally when anypoint in monitor area is in node sensing range then area istotally covered and network coverage ratio is 1 In practicalapplication as nodes are deployed randomly it is possiblethat effective coverage areas will multioverlap as shown inFigure 2
Approximate calculation method on network coverage isas follows dividing monitor area into equal grids if grids aresmall enough then node coverage to grid approximates tothat of to grid center point In this case network coverageratio approximates to nodes coverage to all grid center points
If in monitor area grid number is 119860119892 and node number
is 119860119899 According to Probability Sensing Model the sensing
probability of center point of grids 119866119894sensed by nodes119873
119895is
119901119892119899
(119866119894 119873119895)
=
1 119877119904minus 119903 ge 119889 (119866
119894 119873119895)
119890minus120582sdot120572120573
119877119904minus 119903 lt 119889 (119866
119894 119873119895) lt 119877119904+ 119903
0 119877119904+ 119903 le 119889 (119866
119894 119873119895)
(5)
wherein 119889(119866119894 119873119895) is for distance between center point of
grids 119866119894and nodes 119873
119895 119877119904is for the max sensed radius of
nodes without disruptive factors and parameters 119903 120582 120572 120573
have the same meaning as in formula (1)As it is an independent event that whether center point
of grids 119866119894can be sensed by nodes 119873
119895or not according to
probability theory the probability that grids 119866119894are sensed by
at least one node is
119901119892(119866119894) = 1 minus
119860119899
prod
119895=1
(1 minus 119901119892119899
(119866119894 119873119895)) (6)
In this paper the probability that all center points of grids119866119894in monitor area are sensed by at least one node is
approximated to network coverage ratio 120578
120578 =
sum119860119892
119894=1119901119892(119866119894)
119860119892
(7)
3 Particle Swarm Optimization Algorithm
The network coverage problem can be abstracted as theoptimization goal of the network coverage and the non-constrained optimization problem of the decision variablesis based on the coordinate of the node In this paper theparticle swarm optimization algorithm is used to solve theoptimization problem Because the coordinate value of thedecision variable node is continuous it is different fromthe task assignment problem and the network coverageproblem needs the continuous particle swarm optimizationalgorithm Since the particle swarm optimization algorithmhas been proposed many researchers have put forward manyimproved algorithms based on different practical applica-tions
31 Basic Particle Swarm Optimization Algorithm Particleswarm optimization algorithm is designed from research onbird flock preying behavior Assuming that there is onlyone piece of food in a searching area and that bird flock israndomly distributed in this area without knowing where thefood is and how far away from its location its task is to findthat food Each individual in the bird flock updates its currentposition according to history information of individual aswell as group By updating location constantly the bird flockconfirms the exact location of food thus completing preyingtask The researcher is inspired by bird flock preying modelhence particle swarm optimization algorithm is proposed to
4 Journal of Sensors
solve optimization problem There are solutions in researcharea wherein particle swarm is randomly located in and eachparticle is a potential solution to optimization problemTheseparticles are evaluated by fitness value which is decided byoptimization target function and each particle decides itsownflying speed information according to history best fitnessvalue of its own as well as group and then moves at this speedin entire solution space that is the individual exchangesinformation with other particles in some certain forms to getheuristic information to lead groupmovement hence gettingoptimum solution to optimization problem
Mathematical description on basic PSO algorithm is asfollows
Assuming that population size of particle swarm is 119899decision space is119898 wherein the location of particle 119868 at time119905 denotes119883(119905)
119894= (119909(119905)
1198941 119909(119905)
1198942 119909
(119905)
119894119898) 119894 = 1 2 119899 and speed
of particle 119868 is defined as particle moving distance in eachiteration which is denoted as 119881(119905)
119894= (V(119905)1198941 V(119905)1198942 V(119905)
119894119898) 119894 =
1 2 119899 hence the moving speed and location of particle 119868at time 119905 + 1 in 119889 (119889 = 1 2 119898) space change according tothe formulas below [10]
V(119905+1)119894119889
= 119908 sdot V(119905)119894119889
+ 1198881sdot 1199031sdot (119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032
sdot (119892(119905)
119889minus 119909(119905)
119894119889)
(8)
V(119905+1)119894119889
=
Vmax V(119905+1)119894119889
gt Vmax
minusVmax V(119905+1)119894119889
lt minusVmax(9)
119909(119905+1)
119894119889= 119909(119905)
119894119889+ V(119905+1)119894119889
(10)
wherein in formula (8) 119908 is for inertia weight whichis mainly for producing disturbance to prevent prematureconvergence on algorithm 119888
1and 1198882are for acceleration con-
stants which adjust maximum step size of particle moving tothe best individual particle and the best global particle and 119903
1
and 1199032are two randomnumbers in range [0 1] 119901(119905)
119894119889is for 119889th-
dimensional component of individual extremum 119901best 119892(119905)
119889
is for 119889th-dimensional component of global extremum 119892bestIn formula (9) Vmax is for particle max flight speed whichis a constant and is used to limit particle max flight speedto improve searching result As shown in formulas (8)sim(10)particle moving velocity increment is closely related to itsown history flying experience and group flying experienceand limited by max flight speed [11]
32 Particle SwarmOptimization Algorithmwith CompressionFactor Learning factors 119888
1and 1198882and the particles having a
self-summary to the group of outstanding individual learningability respectively this reflects the exchange of informationbetween the particle swarm If 119888
1is larger the particle will
make more wandering in the local area and if 1198882is larger the
particle will prematurely be converged as a local minimumvalue
In order to control the particle speed effectively makingthe algorithm balanced between global and local optimiza-tion Clerc and Kennedy [12] proposed a constriction factor
PSO algorithm and the speed of the particle update formulawill be changed
V(119905+1)119894119889
= 120593
sdot V(119905)119894119889
+ 1198881sdot 1199031(119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032(119892(119905)
119889minus 119909(119905)
119894119889)
120593 =2
100381610038161003816100381610038162 minus 119862radic1198622 minus 4119862
10038161003816100381610038161003816
119862 = 1198881+ 1198882
(11)
In order to ensure the solution of the algorithm 1198881+
1198882value must be greater than 4 Typical parameters are as
follows
(1) 1198881= 1198882= 205 119862 = 41 and shrinkage factor 120593 is
0729
(2) Particle population size pop = 30 1198881= 28 119888
2= 13 119862
is 41 at this time and the shrinkage factor 120593 is 0729
33 Particle Swarm Optimization Algorithm with ImprovedWeight Inertia weight 119908 is one of the most importantparameters in PSO the global search ability of the algorithmwill be improved with the help of the larger 119908 value and asmall119908 value is to enhance the capacity of local optimizationalgorithm According to different weights 119908 can be dividedinto PSO linearly decreasing weights by adaptive weightmethod and random weight method [13]
Linearly Decreasing Weights [14] Let inertia weight decreaselinearly from the maximum value 119908max to 119908min at thebeginning a larger 119908 value is to optimum algorithm out oflocal conductively and the latter algorithm is in favor of localspace for precise search Inertia weight 119908 relationship withthe number is
119908 = 119908max minus119905 lowast (119908max minus 119908min)
119905max (12)
where 119908max and 119908min denote the inertia weight maximumand minimum values 119905 represents the current numberof iterations and 119905max is the maximum number of itera-tions
Adaptive weight method is that the inertia weight 119908 withthe fitness value of particles is automatically changed Thismethod takes into account the particle current fitness value119891 and the relationship between the average fitness value 119891averand the minimum fitness value 119891min in all particles Whenthe fitness value of all the particles tends to converge or beoptimum the inertia weight 119908 is greater when the fitnessvalue of all the particles scattered inertia weight 119908 takes asmaller value Meanwhile when the fitness value of particlesis better than average fitness value 119891aver this corresponds toa smaller inertia weight when the fitness value of particlesis worse than average fitness value 119891aver this corresponds to
Journal of Sensors 5
a larger inertia weight so that the particles move closer tobetter search area Inertia weight 119908 is expressed as
119908
=
119908max minus(119908max minus 119908min) lowast (119891 minus 119891min)
(119891avg minus 119891min) 119891 le 119891avg
119908max 119891 gt 119891avg
(13)
Random weight method [15] is that the inertia weight 119908obeys a certain random number distributed randomly If atthe beginning of the algorithm the particle position is closeto the best point linearly decreasing the weight of the larger119908 values may deviate from the optimum region and randomweights 119908 may have a relatively small value accelerating theconvergence speed If at the beginning of the algorithm theparticles could not be found in the optimum area the weights119908 method is decreased linearly because of diminishing soultimately the algorithm cannot be converged to the bestadvantage and the randomweightmethod can overcome thislimitation Therefore in practical problems some randomweighting method can get better results than linear declinelaw Inertia weight 119908 is expressed as
119908 = 120583 + 120590 sdot 119873 (0 1)
120583 = 120583min + (120583max minus 120583min) lowast rand(14)
wherein 120583 represents a random weighted mean 120583max and120583min respectively and the minimum and maximum ran-dom weights mean 120590 represents a random weights vari-ance 119873(0 1) represents the standard normal distribution ofrandom numbers and rand represents a random numberbetween 0 and 1
34 Particle Swarm Optimization Algorithm with ImprovedLearning Factor In the practical application of the algorithmthe value of learning the way factor is 119888
1= 1198882= 2 there are
other variable learning factors a common synchronous andasynchronous learning factor is changed
Synchronous learning factor that is changed by 1198881and 1198882
at the same time decreasing linearly their relationship with 119905
is as follows
1198881= 1198882= 119888max minus
119888max minus 119888min119905max
sdot 119905 (15)
where 119888max and 119888min are themaximumandminimum learningfactors usually the maximum value is 21 and the minimumis 08
Asynchronous learning factor changes [16] are 1198881and 1198882
having various changes over time Larger initial algorithmis 1198881 1198882is smaller so that the particles have a greater
self-learning ability and smaller social learning ability theparticles can search the entire search space globally Latersmaller algorithm 119888
1 1198882has larger particles having a smaller
self-learning ability and greater social learning ability the
particles can accurately search the optimum area Learningfactor is expressed in as
1198881= 119888max minus
119888max minus 119888min119905max
sdot 119905
1198882= 119888min +
119888max minus 119888min119905max
sdot 119905
(16)
Ratnaweera et al [17] found experimentally that in mostcases 119888max = 25 119888min = 05 can be taken to achieve the idealsolution
35 Hybrid Particle Swarm Optimization In addition toswarm intelligence algorithm and particle swarm opti-mization algorithm but also including genetic algorithmssimulated annealing algorithm and firefly algorithm eachalgorithm has its unique advantages Hybrid particle swarmoptimization refers to the other intelligent optimizationalgorithms into the ideological hybrid algorithm particleswarm optimization algorithm formation
The genetic algorithm and particle swarm optimizationalgorithm combined GA-PSO algorithm is proposed byPremalatha and Natarajan [18] The genetic algorithm ofnatural selection mechanism (Selection) applied to PSOthe basic idea is that in each iteration all the particles aresorted according to their fitness values and a good half ofthe particles are of fitness location and speed value ratherthan another half that are sorted according to the positionand velocity of a particle while maintaining all particlesfitness unchanged By eliminating the difference betweenthe particles the algorithm can achieve faster convergenceHybrid genetic algorithm mechanism (crossover) applied toPSO is that in each iteration randomly select a fixed numberof particles into the hybrid cell the particles cross the poolpairwise hybridization to give the same number of progenyparticles with particle replacing the parent progeny particlesiteration populationWherein the position and velocity of theparticle and offspring (18) is determined by formula (17)
119909child = 119901 sdot 119909parent1 + (1 minus 119901) sdot 119909parent2 (17)
Vchild =
Vparent1 + Vparent210038161003816100381610038161003816Vparent1 + Vparent2
10038161003816100381610038161003816
sdot10038161003816100381610038161003816Vparent
10038161003816100381610038161003816 (18)
wherein119901 is a randomnumber [0 1] and Vparent can be chosenrandomly as Vparent1 or Vparent2 By hybridization technologyit can improve particle swarm diversity avoiding prematureconvergence algorithm
Liu et al [19] proposed the chaotic particle swarm opti-mization algorithm in order to optimize the particle swarmoptimization algorithm Chaos (chaos) is a nonlinear phe-nomenon in nature in a ubiquitous periodicity randomnessand intrinsic regularity Periodicity of chaos embodied in itcannot be repeated through all the states in a search spacerandomness is reflected in its performance similar to messyrandom variable which embodies the inherent regularity innonlinear systems under certain conditions defined in it Inaddition the chaotic initial conditions that are particularlysensitive to the initial value of the extremely weak changes
6 Journal of Sensors
will cause a huge deviation in the system Because chaos iseasy to implement andmake the algorithmout of local optimaspecial properties the researchers propose a chaotic opti-mization idea Periodicity of chaos randomness and chaosinherent regularity of such thinking can be complementaryoptimization algorithm combined with PSO
Victoire and Jeyakumar [20] proposed PSO and sequen-tial quadratic programming (SQP) method for solving thecombined economic dispatch (economic dispatch problemEDP) SQP is a nonlinear programming method it startsfrom a single point of search and uses gradient informationobtained final solution Research by three different EDPquestions the validity of the method
Lu et al [21] have introduced the real value of themutation operator (real-valued mutation RVM) into theparticle swarm optimization algorithm the algorithm is usedto improve the global search ability Interestingly whenthe RVM operator is applied to different functions it canbe operated effectively By comparing the experiments theauthors found that a combination of shrinkage factor inertiaweight and RVM operator mixed CBPSO-RVM algorithmcan perform better in most of the test cases
4 Particle Swarm Optimization AlgorithmFused with Idea from Simulated Annealing
Particle swarm optimization algorithm can be easily trappedin the local optimum and result in premature convergenceProbabilistic jumping property of simulated annealing SAmakes it possible to complementary associate with particleswarm optimization algorithm and fuses PSO global explo-ration capacity with SA local exploration capacity
Annealing in metallurgy refers to heating and thencooling the material at a specific rate which is for increasingthe volume of crystal grains and reducing defects in thecrystal lattice At the beginning material atom is at a positionwhich has local minimum internal energy then heatingincreases atoms energy and atoms leave the initial positionand move randomly to other locations When annealingcools down atoms are with low speed so it is possiblefor atoms to find a location with lower internal energythan initial ones Inspired by annealing of metals researcherproposes simulated annealing to solve optimization prob-lem Optimization problem searches every potential solutionto represent atoms location and evaluation function forpotential solution represents atoms internal energy at currentlocation wherein the optimization purpose is to find anoptimization solution hence getting a minimum value forevaluation function of this solution
Simulated annealing is with mutation probability insearching process which can effectively avoid the algorithmbeing trapped in the local optimum in iteration process Thekey to this algorithm is to refuse local minimum solution incertain probability and then skip over local minimum pointand continue to search other possible solutions in search areaalso the probability decreases along with temperature
This paper fuses particle swarm optimization algorithmand simulated annealing to solve coverage restoring problem
in wireless sensor actuator network Algorithm detailed stepsare as below
Step 1 Initialize basic parameters like population size themaximum number of iterations inertia weight learning fac-tor annealing constant and so on Set upper as well as lowerbounds for particle location and particle speed Initialize eachparticle location in swarm as all nodes coordinate in networkwith coverage and randomly initialize each particle speed
Step 2 Calculate fitness value 119891(119901119894) of each particle 119901
119894 Take
current location and fitness value of each particle as its historybest location and fitness value 119901best Use location of particle119901119892with best fitness value as swarm history best location and
corresponding best fitness value 119891(119901119892) as swarm best fitness
value
Step 3 Determine initial temperature according to the for-mula
1198790=
119891 (119901119892)
ln 5 (19)
Step 4 According to fitness value 119891(119901119894) and global best value
119891(119901119892) of each particle119901
119894 calculate fitted value of each particle
fitness value under current temperature
TF (119901119894) =
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
sumpop119894=1
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
(20)
Step 5 According to fitted value of each particle fitness valuefuse with roulette strategy and confirm replacement value119901119903
119892of global optimal particle 119901
119892from all particles Then
substitute fitted value into particle moving update equationto solve particle new speed and new location for applying innext iteration
Step 6 Calculate fitness value of each particle and updateparticles 119901best and swarm 119892best
Step 7 Operate annealing according to formula (21) wherein120582 is for annealing constant and 119896 is for iterative times
119879119896+1
= 120582 sdot 119879119896 (21)
Step 8 If the algorithm reaches either predicted operationalprecision or max iterative times then algorithm ends Orreturn to Step 4
5 Simulation Experiment
51 Particle Parameter Description Coverage restoring prob-lem can be abstracted into nonconstrained optimizationproblem which takes network coverage ratio as optimiza-tion target and nodes coordinates as decision variable Thischapter describes particle parameter Particle location X isfor all nodes coordinates which can be expressed as X =
1199091 1199101 1199092 1199102 119909
119894 119910119894 119909
119873 119910119873 wherein 119873 is for nodes
number and 119909119894 119910119894(1 le 119894 le 119873) are for abscissa and ordinate of
Journal of Sensors 7
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8456
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x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 3 The initial deployment of nodes
particle 119894 Monitor area is a square two-dimensional regionwherein origin of coordinate is square vertex at the lowerleft corner so both abscissa and ordinate of particle satisfy0 le 119909119894 119910119894le 119871 wherein 119871 is for side length of monitor area
Particle velocity V is for incremental of particle locationand can be expressed as V = V
1199091 V1199101 V1199092 V1199102 V
119909119894
V119910119894 V
119909119899 V119910119899 wherein each dimension element value of
velocity is corresponding to each dimension element valueof position and indicates corresponding coordinate valueschange To limit particle velocity upper Vmax and lower Vminbounds of particle velocity need to be set
Particle fitness value function is reciprocal value ofnetwork coverage based on gridswhich arementioned in Sec-tion 22 as shown in formula (22) So algorithm solving targetis network nodes coordinate distributionwhichminimize thefitness function value
min fitness = 1
120578=
119860119892
sum119860119892
119894=1119901119892(119866119894)
(22)
52 Experiment Result andAnalysis In this paper the solvingmethod for coverage restoring problem is simulated inMAT-LAB 2012a as experimental environment Nodes number119873 =
100 and monitor area side length 119871 = 500m nodes sensingradius 119877
119904= 30m nodes possibility sensing model parameter
119903 = 6m 120582 = 120573 = 05 and grids number 119860119892= 100 During
initialization nodes are deployed randomly and evenly inwhole monitor area and initial deployment of nodes is asshown in Figure 3 In this figure every dot is for nodesnumber beside is for node number and circle region is fornodes sensing region As shown in the figure there are 4obvious holes in initial deployment of nodes and the solvingtarget of network coverage problem is to move redundantnodes beside holes hence increasing network coverage
To verify effectiveness of particle swarm optimizationalgorithm which is based on simulated annealing this paperuses basic particle swarmoptimization algorithm and variousimproved algorithms to simulate and compare on network
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9 10
11
12
13
14
15
1617
18
193191
20
21
22
23
24
25
26
27
28
29
30
32
33
34
3536
3738
39
40
41
42
43
44
45
46
47
48
49
50
52
5354
5557
5158
59
60
61
62
63
64
65
66
67
68
69
70
7172
73
74
75
5676
77
78
79
80
8182
83
84
85
86
87
88
89
90
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 4 The final deployment of nodes (BPSO)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
921527
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 5 The final deployment of nodes (GPSOmdashcrossover)
coverage problem Figures 4ndash7 are the final deployments ofnodes which are simulated from basic particle swarm opti-mization algorithm particle swarm optimization algorithmfused with crossover mutation idea from genetic algorithmparticle swarm optimization algorithm based on simulatedannealing and with compression factor and particle swarmoptimization algorithm based on simulated annealing andusing asynchronous learning factors Figure 8 is comparisonon best fitness value change in iteration process of eachalgorithm
After analyzing simulation results from each algorithmwe can see that simulation effect fromGPSO is the worst andSAPSOwith compression factor is the bestThe final purposeof particle movement is to improve network coverage bymoving redundant node and restoring network holes atthe meantime to avoid too much energy consumptionmoving distance of redundant node cannot be too far Ineach algorithm the nodes moving distance is controlled byparticle upper Vmax and lower Vmin bounds According to
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
45
46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
23
24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
43
44
45
46
47
48
50
51
52
5354 55
56
57
58
59
60
61
62
64
65
66
67
68
6971
72
7374
75
76
77
7899
79
80
8182
83
84
85
86
87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
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DistributedSensor Networks
International Journal of
2 Journal of Sensors
which establishes two-way connection zoning topologybuilds the largest backbone around damaged area center andthen deploys the relay nodes (RNs) to connect each partitionto the backbone outer polygon Simulation states that thisalgorithm can get topology with high coverage by placingless relay nodes With distributed self-deployment strategySenturk et al [6] recover continuity of zone wireless sensornetwork and proposes two methods to locate relay nodeswherein the first one is based onmovement of relay nodes vir-tual force and the second one is based on game theory in zoneguiding nodes Simulation states that in most situations themethod based on game theory performs better than the oneon virtual force Aiming at the coverage decrease problemdueto the failure of many nodes in network Zhao and Wang [7]propose a flow-based multiobjective nonlinear mathematicalprogramming model which decreases coverage by movingnodes in network takes the total travel distance of nodes andsingle travel distance as optimization target and then usesflow equilibrium conditions to restore network coverage
As current improvement on integrated circuit technologyleads to lower energy consumption on sensor and processorrelatively the communication energy consumption betweennodes becomes too low to consider So when calculating theenergy consumption the communication energy consump-tion can be ignored Move energy consumption is defined asthe energy consumed when attack node moves towards bestattack point so move energy consumption is proportional tothe distance that attack nodes moves in hence distance thatattack nodes moves in can be used to calculate move energyconsumption directly
2 Models for Problem Solving
21 Node Sensing Model Node Sensing Model [8 9] isa prior problem in network coverage control technologyThree main perception models have been used in recentresearch work which include Circumference Sensing ModelProbability Sensing Model and Direction Sensing ModelCircumference SensingModel defines nodes sensing range asa round enclosed area which takes nodes location as centerand sensing radius 119877
119904as radius The sensing radius 119877
119904is
decided by physical characteristics of the sensor Any pointin this round area can be sensed by node
Circumference Sensing Model assumes that uncertaintydoes not exist when the sensor senses target area But inpractical application due to the disruptive factors such asambient noise obstacle and the feature that wireless signalintensity decays along with the communication distanceincrease circumference Sensing Model cannot reflect nodessensing feature well Probability Sensing Model considersthe uncertainty of node sensing in practical applicationwherein the probability that an intruder 119889 sensed by node 119899is expressed as119901119904(119899 119889)
=
1 119877119904minus 119903 ge
1003817100381710038171003817(119909119899 119910119899) minus (119909119889 119910119889)1003817100381710038171003817
119890minus120582sdot120572120573
119877119904minus 119903 le
1003817100381710038171003817(119909119899 119910119899) minus (119909119889 119910119889)1003817100381710038171003817 le 119877119904+ 119903
0 119877119904+ 119903 le
1003817100381710038171003817(119909119899 119910119899) minus (119909119889 119910119889)1003817100381710038171003817
(1)
Determineperceived area
Uncertaintyperception area
R s+r
Rsrr
Rsminusr
Figure 1 Probability Sensing Model
In this formula 119877119904is for the max sensed radius without
disruptive factors 119903 is for measuring nodes uncertain moni-toring ability Arguments 120572 = (119909
119899 119910119899) minus (119909
119889 119910119889) minus (119877
119904minus 119903)
wherein 120582 and 120573 are for intruder sensed probability value bynode when intruder is in uncertainmonitoring area Physicalcharacteristic of Probability Sensing Model is as shown inFigure 1
Sensing direction of the two Sensing Models is omni-direction But in practical application some sensors havecertain direction wherein only when intruder is in certaindirection of nodes can they be sensed The Node SensingModel setup under this feature is called Directed SendingModel
22 Related Definitions
Definition 1 (effective coverage area) Supposing an intrudercan be sensed by node at any point in designated area thenthe designated area is called coverage area 120595(119894) of node 119894Effective coverage area 119894 is defined as intersection of coveragearea 120595(119894) and monitor areaΩ
120585 (119894) = 120595 (119894) cap Ω (2)
Definition 2 (coverage ratio) Coverage ratio of node 119894 isdefined as the area ratio of effective node coverage area 120585(119894)to monitor area Ω Network coverage ratio is defined as thearea ratio of the union of all node effective coverage areasin monitor area Network coverage ratio is an importantindicator of the quality of network coverage
120578 =119878 (⋃119894120585 (119894))
119878 (Ω) (3)
Definition 3 (connectivity) If two nodes can communicatethrough single-hop or multi-hop network then they arecalled connected Supposing that the total number of nodes inmonitor area is 119899 obviously the nodes number 120577(119894) connected
Journal of Sensors 3
O4 O1
O3
O2
Figure 2 The multioverlapping of coverage region
with node 119894 will satisfy the formula 0 le 120577(119894) le 119899 minus 1 If allnodes can communicate between each other then the totalnumber of communication paths is 119899(119899 minus 1)2 Connectivityof network is defined as the total number ratio of currentcommunication path to max communication path
120591 =12 sdot sum
119894120577 (119894)
119899 (119899 minus 1) 2=
sum119894120577 (119894)
119899 (119899 minus 1) (4)
When doing research on network coverage problem thepaper supposes that network and nodes have the followingcharacteristics
(1) Nodes in network are isomorphic and movable andhave unique short addresses to identify themselves
(2) Sensing model of nodes is Probability SensingModelwhich has the same sensing radius 119877
119904and communi-
cation radius 119877119888 andmeets 119877
119888ge 2 sdot119877
119904 When it meets
this condition network coverage problem is of equalvalue to connection problem
Monitor area is a square area with side length 119871and 119873 nodes are randomly and evenly deployed inmonitor area
(3) Each node gets its own location information fromself-positioning of network and then broadcasts to theentire network
23 Network Coverage Based on Grids Ideally when anypoint in monitor area is in node sensing range then area istotally covered and network coverage ratio is 1 In practicalapplication as nodes are deployed randomly it is possiblethat effective coverage areas will multioverlap as shown inFigure 2
Approximate calculation method on network coverage isas follows dividing monitor area into equal grids if grids aresmall enough then node coverage to grid approximates tothat of to grid center point In this case network coverageratio approximates to nodes coverage to all grid center points
If in monitor area grid number is 119860119892 and node number
is 119860119899 According to Probability Sensing Model the sensing
probability of center point of grids 119866119894sensed by nodes119873
119895is
119901119892119899
(119866119894 119873119895)
=
1 119877119904minus 119903 ge 119889 (119866
119894 119873119895)
119890minus120582sdot120572120573
119877119904minus 119903 lt 119889 (119866
119894 119873119895) lt 119877119904+ 119903
0 119877119904+ 119903 le 119889 (119866
119894 119873119895)
(5)
wherein 119889(119866119894 119873119895) is for distance between center point of
grids 119866119894and nodes 119873
119895 119877119904is for the max sensed radius of
nodes without disruptive factors and parameters 119903 120582 120572 120573
have the same meaning as in formula (1)As it is an independent event that whether center point
of grids 119866119894can be sensed by nodes 119873
119895or not according to
probability theory the probability that grids 119866119894are sensed by
at least one node is
119901119892(119866119894) = 1 minus
119860119899
prod
119895=1
(1 minus 119901119892119899
(119866119894 119873119895)) (6)
In this paper the probability that all center points of grids119866119894in monitor area are sensed by at least one node is
approximated to network coverage ratio 120578
120578 =
sum119860119892
119894=1119901119892(119866119894)
119860119892
(7)
3 Particle Swarm Optimization Algorithm
The network coverage problem can be abstracted as theoptimization goal of the network coverage and the non-constrained optimization problem of the decision variablesis based on the coordinate of the node In this paper theparticle swarm optimization algorithm is used to solve theoptimization problem Because the coordinate value of thedecision variable node is continuous it is different fromthe task assignment problem and the network coverageproblem needs the continuous particle swarm optimizationalgorithm Since the particle swarm optimization algorithmhas been proposed many researchers have put forward manyimproved algorithms based on different practical applica-tions
31 Basic Particle Swarm Optimization Algorithm Particleswarm optimization algorithm is designed from research onbird flock preying behavior Assuming that there is onlyone piece of food in a searching area and that bird flock israndomly distributed in this area without knowing where thefood is and how far away from its location its task is to findthat food Each individual in the bird flock updates its currentposition according to history information of individual aswell as group By updating location constantly the bird flockconfirms the exact location of food thus completing preyingtask The researcher is inspired by bird flock preying modelhence particle swarm optimization algorithm is proposed to
4 Journal of Sensors
solve optimization problem There are solutions in researcharea wherein particle swarm is randomly located in and eachparticle is a potential solution to optimization problemTheseparticles are evaluated by fitness value which is decided byoptimization target function and each particle decides itsownflying speed information according to history best fitnessvalue of its own as well as group and then moves at this speedin entire solution space that is the individual exchangesinformation with other particles in some certain forms to getheuristic information to lead groupmovement hence gettingoptimum solution to optimization problem
Mathematical description on basic PSO algorithm is asfollows
Assuming that population size of particle swarm is 119899decision space is119898 wherein the location of particle 119868 at time119905 denotes119883(119905)
119894= (119909(119905)
1198941 119909(119905)
1198942 119909
(119905)
119894119898) 119894 = 1 2 119899 and speed
of particle 119868 is defined as particle moving distance in eachiteration which is denoted as 119881(119905)
119894= (V(119905)1198941 V(119905)1198942 V(119905)
119894119898) 119894 =
1 2 119899 hence the moving speed and location of particle 119868at time 119905 + 1 in 119889 (119889 = 1 2 119898) space change according tothe formulas below [10]
V(119905+1)119894119889
= 119908 sdot V(119905)119894119889
+ 1198881sdot 1199031sdot (119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032
sdot (119892(119905)
119889minus 119909(119905)
119894119889)
(8)
V(119905+1)119894119889
=
Vmax V(119905+1)119894119889
gt Vmax
minusVmax V(119905+1)119894119889
lt minusVmax(9)
119909(119905+1)
119894119889= 119909(119905)
119894119889+ V(119905+1)119894119889
(10)
wherein in formula (8) 119908 is for inertia weight whichis mainly for producing disturbance to prevent prematureconvergence on algorithm 119888
1and 1198882are for acceleration con-
stants which adjust maximum step size of particle moving tothe best individual particle and the best global particle and 119903
1
and 1199032are two randomnumbers in range [0 1] 119901(119905)
119894119889is for 119889th-
dimensional component of individual extremum 119901best 119892(119905)
119889
is for 119889th-dimensional component of global extremum 119892bestIn formula (9) Vmax is for particle max flight speed whichis a constant and is used to limit particle max flight speedto improve searching result As shown in formulas (8)sim(10)particle moving velocity increment is closely related to itsown history flying experience and group flying experienceand limited by max flight speed [11]
32 Particle SwarmOptimization Algorithmwith CompressionFactor Learning factors 119888
1and 1198882and the particles having a
self-summary to the group of outstanding individual learningability respectively this reflects the exchange of informationbetween the particle swarm If 119888
1is larger the particle will
make more wandering in the local area and if 1198882is larger the
particle will prematurely be converged as a local minimumvalue
In order to control the particle speed effectively makingthe algorithm balanced between global and local optimiza-tion Clerc and Kennedy [12] proposed a constriction factor
PSO algorithm and the speed of the particle update formulawill be changed
V(119905+1)119894119889
= 120593
sdot V(119905)119894119889
+ 1198881sdot 1199031(119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032(119892(119905)
119889minus 119909(119905)
119894119889)
120593 =2
100381610038161003816100381610038162 minus 119862radic1198622 minus 4119862
10038161003816100381610038161003816
119862 = 1198881+ 1198882
(11)
In order to ensure the solution of the algorithm 1198881+
1198882value must be greater than 4 Typical parameters are as
follows
(1) 1198881= 1198882= 205 119862 = 41 and shrinkage factor 120593 is
0729
(2) Particle population size pop = 30 1198881= 28 119888
2= 13 119862
is 41 at this time and the shrinkage factor 120593 is 0729
33 Particle Swarm Optimization Algorithm with ImprovedWeight Inertia weight 119908 is one of the most importantparameters in PSO the global search ability of the algorithmwill be improved with the help of the larger 119908 value and asmall119908 value is to enhance the capacity of local optimizationalgorithm According to different weights 119908 can be dividedinto PSO linearly decreasing weights by adaptive weightmethod and random weight method [13]
Linearly Decreasing Weights [14] Let inertia weight decreaselinearly from the maximum value 119908max to 119908min at thebeginning a larger 119908 value is to optimum algorithm out oflocal conductively and the latter algorithm is in favor of localspace for precise search Inertia weight 119908 relationship withthe number is
119908 = 119908max minus119905 lowast (119908max minus 119908min)
119905max (12)
where 119908max and 119908min denote the inertia weight maximumand minimum values 119905 represents the current numberof iterations and 119905max is the maximum number of itera-tions
Adaptive weight method is that the inertia weight 119908 withthe fitness value of particles is automatically changed Thismethod takes into account the particle current fitness value119891 and the relationship between the average fitness value 119891averand the minimum fitness value 119891min in all particles Whenthe fitness value of all the particles tends to converge or beoptimum the inertia weight 119908 is greater when the fitnessvalue of all the particles scattered inertia weight 119908 takes asmaller value Meanwhile when the fitness value of particlesis better than average fitness value 119891aver this corresponds toa smaller inertia weight when the fitness value of particlesis worse than average fitness value 119891aver this corresponds to
Journal of Sensors 5
a larger inertia weight so that the particles move closer tobetter search area Inertia weight 119908 is expressed as
119908
=
119908max minus(119908max minus 119908min) lowast (119891 minus 119891min)
(119891avg minus 119891min) 119891 le 119891avg
119908max 119891 gt 119891avg
(13)
Random weight method [15] is that the inertia weight 119908obeys a certain random number distributed randomly If atthe beginning of the algorithm the particle position is closeto the best point linearly decreasing the weight of the larger119908 values may deviate from the optimum region and randomweights 119908 may have a relatively small value accelerating theconvergence speed If at the beginning of the algorithm theparticles could not be found in the optimum area the weights119908 method is decreased linearly because of diminishing soultimately the algorithm cannot be converged to the bestadvantage and the randomweightmethod can overcome thislimitation Therefore in practical problems some randomweighting method can get better results than linear declinelaw Inertia weight 119908 is expressed as
119908 = 120583 + 120590 sdot 119873 (0 1)
120583 = 120583min + (120583max minus 120583min) lowast rand(14)
wherein 120583 represents a random weighted mean 120583max and120583min respectively and the minimum and maximum ran-dom weights mean 120590 represents a random weights vari-ance 119873(0 1) represents the standard normal distribution ofrandom numbers and rand represents a random numberbetween 0 and 1
34 Particle Swarm Optimization Algorithm with ImprovedLearning Factor In the practical application of the algorithmthe value of learning the way factor is 119888
1= 1198882= 2 there are
other variable learning factors a common synchronous andasynchronous learning factor is changed
Synchronous learning factor that is changed by 1198881and 1198882
at the same time decreasing linearly their relationship with 119905
is as follows
1198881= 1198882= 119888max minus
119888max minus 119888min119905max
sdot 119905 (15)
where 119888max and 119888min are themaximumandminimum learningfactors usually the maximum value is 21 and the minimumis 08
Asynchronous learning factor changes [16] are 1198881and 1198882
having various changes over time Larger initial algorithmis 1198881 1198882is smaller so that the particles have a greater
self-learning ability and smaller social learning ability theparticles can search the entire search space globally Latersmaller algorithm 119888
1 1198882has larger particles having a smaller
self-learning ability and greater social learning ability the
particles can accurately search the optimum area Learningfactor is expressed in as
1198881= 119888max minus
119888max minus 119888min119905max
sdot 119905
1198882= 119888min +
119888max minus 119888min119905max
sdot 119905
(16)
Ratnaweera et al [17] found experimentally that in mostcases 119888max = 25 119888min = 05 can be taken to achieve the idealsolution
35 Hybrid Particle Swarm Optimization In addition toswarm intelligence algorithm and particle swarm opti-mization algorithm but also including genetic algorithmssimulated annealing algorithm and firefly algorithm eachalgorithm has its unique advantages Hybrid particle swarmoptimization refers to the other intelligent optimizationalgorithms into the ideological hybrid algorithm particleswarm optimization algorithm formation
The genetic algorithm and particle swarm optimizationalgorithm combined GA-PSO algorithm is proposed byPremalatha and Natarajan [18] The genetic algorithm ofnatural selection mechanism (Selection) applied to PSOthe basic idea is that in each iteration all the particles aresorted according to their fitness values and a good half ofthe particles are of fitness location and speed value ratherthan another half that are sorted according to the positionand velocity of a particle while maintaining all particlesfitness unchanged By eliminating the difference betweenthe particles the algorithm can achieve faster convergenceHybrid genetic algorithm mechanism (crossover) applied toPSO is that in each iteration randomly select a fixed numberof particles into the hybrid cell the particles cross the poolpairwise hybridization to give the same number of progenyparticles with particle replacing the parent progeny particlesiteration populationWherein the position and velocity of theparticle and offspring (18) is determined by formula (17)
119909child = 119901 sdot 119909parent1 + (1 minus 119901) sdot 119909parent2 (17)
Vchild =
Vparent1 + Vparent210038161003816100381610038161003816Vparent1 + Vparent2
10038161003816100381610038161003816
sdot10038161003816100381610038161003816Vparent
10038161003816100381610038161003816 (18)
wherein119901 is a randomnumber [0 1] and Vparent can be chosenrandomly as Vparent1 or Vparent2 By hybridization technologyit can improve particle swarm diversity avoiding prematureconvergence algorithm
Liu et al [19] proposed the chaotic particle swarm opti-mization algorithm in order to optimize the particle swarmoptimization algorithm Chaos (chaos) is a nonlinear phe-nomenon in nature in a ubiquitous periodicity randomnessand intrinsic regularity Periodicity of chaos embodied in itcannot be repeated through all the states in a search spacerandomness is reflected in its performance similar to messyrandom variable which embodies the inherent regularity innonlinear systems under certain conditions defined in it Inaddition the chaotic initial conditions that are particularlysensitive to the initial value of the extremely weak changes
6 Journal of Sensors
will cause a huge deviation in the system Because chaos iseasy to implement andmake the algorithmout of local optimaspecial properties the researchers propose a chaotic opti-mization idea Periodicity of chaos randomness and chaosinherent regularity of such thinking can be complementaryoptimization algorithm combined with PSO
Victoire and Jeyakumar [20] proposed PSO and sequen-tial quadratic programming (SQP) method for solving thecombined economic dispatch (economic dispatch problemEDP) SQP is a nonlinear programming method it startsfrom a single point of search and uses gradient informationobtained final solution Research by three different EDPquestions the validity of the method
Lu et al [21] have introduced the real value of themutation operator (real-valued mutation RVM) into theparticle swarm optimization algorithm the algorithm is usedto improve the global search ability Interestingly whenthe RVM operator is applied to different functions it canbe operated effectively By comparing the experiments theauthors found that a combination of shrinkage factor inertiaweight and RVM operator mixed CBPSO-RVM algorithmcan perform better in most of the test cases
4 Particle Swarm Optimization AlgorithmFused with Idea from Simulated Annealing
Particle swarm optimization algorithm can be easily trappedin the local optimum and result in premature convergenceProbabilistic jumping property of simulated annealing SAmakes it possible to complementary associate with particleswarm optimization algorithm and fuses PSO global explo-ration capacity with SA local exploration capacity
Annealing in metallurgy refers to heating and thencooling the material at a specific rate which is for increasingthe volume of crystal grains and reducing defects in thecrystal lattice At the beginning material atom is at a positionwhich has local minimum internal energy then heatingincreases atoms energy and atoms leave the initial positionand move randomly to other locations When annealingcools down atoms are with low speed so it is possiblefor atoms to find a location with lower internal energythan initial ones Inspired by annealing of metals researcherproposes simulated annealing to solve optimization prob-lem Optimization problem searches every potential solutionto represent atoms location and evaluation function forpotential solution represents atoms internal energy at currentlocation wherein the optimization purpose is to find anoptimization solution hence getting a minimum value forevaluation function of this solution
Simulated annealing is with mutation probability insearching process which can effectively avoid the algorithmbeing trapped in the local optimum in iteration process Thekey to this algorithm is to refuse local minimum solution incertain probability and then skip over local minimum pointand continue to search other possible solutions in search areaalso the probability decreases along with temperature
This paper fuses particle swarm optimization algorithmand simulated annealing to solve coverage restoring problem
in wireless sensor actuator network Algorithm detailed stepsare as below
Step 1 Initialize basic parameters like population size themaximum number of iterations inertia weight learning fac-tor annealing constant and so on Set upper as well as lowerbounds for particle location and particle speed Initialize eachparticle location in swarm as all nodes coordinate in networkwith coverage and randomly initialize each particle speed
Step 2 Calculate fitness value 119891(119901119894) of each particle 119901
119894 Take
current location and fitness value of each particle as its historybest location and fitness value 119901best Use location of particle119901119892with best fitness value as swarm history best location and
corresponding best fitness value 119891(119901119892) as swarm best fitness
value
Step 3 Determine initial temperature according to the for-mula
1198790=
119891 (119901119892)
ln 5 (19)
Step 4 According to fitness value 119891(119901119894) and global best value
119891(119901119892) of each particle119901
119894 calculate fitted value of each particle
fitness value under current temperature
TF (119901119894) =
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
sumpop119894=1
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
(20)
Step 5 According to fitted value of each particle fitness valuefuse with roulette strategy and confirm replacement value119901119903
119892of global optimal particle 119901
119892from all particles Then
substitute fitted value into particle moving update equationto solve particle new speed and new location for applying innext iteration
Step 6 Calculate fitness value of each particle and updateparticles 119901best and swarm 119892best
Step 7 Operate annealing according to formula (21) wherein120582 is for annealing constant and 119896 is for iterative times
119879119896+1
= 120582 sdot 119879119896 (21)
Step 8 If the algorithm reaches either predicted operationalprecision or max iterative times then algorithm ends Orreturn to Step 4
5 Simulation Experiment
51 Particle Parameter Description Coverage restoring prob-lem can be abstracted into nonconstrained optimizationproblem which takes network coverage ratio as optimiza-tion target and nodes coordinates as decision variable Thischapter describes particle parameter Particle location X isfor all nodes coordinates which can be expressed as X =
1199091 1199101 1199092 1199102 119909
119894 119910119894 119909
119873 119910119873 wherein 119873 is for nodes
number and 119909119894 119910119894(1 le 119894 le 119873) are for abscissa and ordinate of
Journal of Sensors 7
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
1527
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 3 The initial deployment of nodes
particle 119894 Monitor area is a square two-dimensional regionwherein origin of coordinate is square vertex at the lowerleft corner so both abscissa and ordinate of particle satisfy0 le 119909119894 119910119894le 119871 wherein 119871 is for side length of monitor area
Particle velocity V is for incremental of particle locationand can be expressed as V = V
1199091 V1199101 V1199092 V1199102 V
119909119894
V119910119894 V
119909119899 V119910119899 wherein each dimension element value of
velocity is corresponding to each dimension element valueof position and indicates corresponding coordinate valueschange To limit particle velocity upper Vmax and lower Vminbounds of particle velocity need to be set
Particle fitness value function is reciprocal value ofnetwork coverage based on gridswhich arementioned in Sec-tion 22 as shown in formula (22) So algorithm solving targetis network nodes coordinate distributionwhichminimize thefitness function value
min fitness = 1
120578=
119860119892
sum119860119892
119894=1119901119892(119866119894)
(22)
52 Experiment Result andAnalysis In this paper the solvingmethod for coverage restoring problem is simulated inMAT-LAB 2012a as experimental environment Nodes number119873 =
100 and monitor area side length 119871 = 500m nodes sensingradius 119877
119904= 30m nodes possibility sensing model parameter
119903 = 6m 120582 = 120573 = 05 and grids number 119860119892= 100 During
initialization nodes are deployed randomly and evenly inwhole monitor area and initial deployment of nodes is asshown in Figure 3 In this figure every dot is for nodesnumber beside is for node number and circle region is fornodes sensing region As shown in the figure there are 4obvious holes in initial deployment of nodes and the solvingtarget of network coverage problem is to move redundantnodes beside holes hence increasing network coverage
To verify effectiveness of particle swarm optimizationalgorithm which is based on simulated annealing this paperuses basic particle swarmoptimization algorithm and variousimproved algorithms to simulate and compare on network
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
5001
2
3
4
56
7
8
9 10
11
12
13
14
15
1617
18
193191
20
21
22
23
24
25
26
27
28
29
30
32
33
34
3536
3738
39
40
41
42
43
44
45
46
47
48
49
50
52
5354
5557
5158
59
60
61
62
63
64
65
66
67
68
69
70
7172
73
74
75
5676
77
78
79
80
8182
83
84
85
86
87
88
89
90
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 4 The final deployment of nodes (BPSO)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
921527
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 5 The final deployment of nodes (GPSOmdashcrossover)
coverage problem Figures 4ndash7 are the final deployments ofnodes which are simulated from basic particle swarm opti-mization algorithm particle swarm optimization algorithmfused with crossover mutation idea from genetic algorithmparticle swarm optimization algorithm based on simulatedannealing and with compression factor and particle swarmoptimization algorithm based on simulated annealing andusing asynchronous learning factors Figure 8 is comparisonon best fitness value change in iteration process of eachalgorithm
After analyzing simulation results from each algorithmwe can see that simulation effect fromGPSO is the worst andSAPSOwith compression factor is the bestThe final purposeof particle movement is to improve network coverage bymoving redundant node and restoring network holes atthe meantime to avoid too much energy consumptionmoving distance of redundant node cannot be too far Ineach algorithm the nodes moving distance is controlled byparticle upper Vmax and lower Vmin bounds According to
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
45
46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
23
24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
43
44
45
46
47
48
50
51
52
5354 55
56
57
58
59
60
61
62
64
65
66
67
68
6971
72
7374
75
76
77
7899
79
80
8182
83
84
85
86
87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
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DistributedSensor Networks
International Journal of
Journal of Sensors 3
O4 O1
O3
O2
Figure 2 The multioverlapping of coverage region
with node 119894 will satisfy the formula 0 le 120577(119894) le 119899 minus 1 If allnodes can communicate between each other then the totalnumber of communication paths is 119899(119899 minus 1)2 Connectivityof network is defined as the total number ratio of currentcommunication path to max communication path
120591 =12 sdot sum
119894120577 (119894)
119899 (119899 minus 1) 2=
sum119894120577 (119894)
119899 (119899 minus 1) (4)
When doing research on network coverage problem thepaper supposes that network and nodes have the followingcharacteristics
(1) Nodes in network are isomorphic and movable andhave unique short addresses to identify themselves
(2) Sensing model of nodes is Probability SensingModelwhich has the same sensing radius 119877
119904and communi-
cation radius 119877119888 andmeets 119877
119888ge 2 sdot119877
119904 When it meets
this condition network coverage problem is of equalvalue to connection problem
Monitor area is a square area with side length 119871and 119873 nodes are randomly and evenly deployed inmonitor area
(3) Each node gets its own location information fromself-positioning of network and then broadcasts to theentire network
23 Network Coverage Based on Grids Ideally when anypoint in monitor area is in node sensing range then area istotally covered and network coverage ratio is 1 In practicalapplication as nodes are deployed randomly it is possiblethat effective coverage areas will multioverlap as shown inFigure 2
Approximate calculation method on network coverage isas follows dividing monitor area into equal grids if grids aresmall enough then node coverage to grid approximates tothat of to grid center point In this case network coverageratio approximates to nodes coverage to all grid center points
If in monitor area grid number is 119860119892 and node number
is 119860119899 According to Probability Sensing Model the sensing
probability of center point of grids 119866119894sensed by nodes119873
119895is
119901119892119899
(119866119894 119873119895)
=
1 119877119904minus 119903 ge 119889 (119866
119894 119873119895)
119890minus120582sdot120572120573
119877119904minus 119903 lt 119889 (119866
119894 119873119895) lt 119877119904+ 119903
0 119877119904+ 119903 le 119889 (119866
119894 119873119895)
(5)
wherein 119889(119866119894 119873119895) is for distance between center point of
grids 119866119894and nodes 119873
119895 119877119904is for the max sensed radius of
nodes without disruptive factors and parameters 119903 120582 120572 120573
have the same meaning as in formula (1)As it is an independent event that whether center point
of grids 119866119894can be sensed by nodes 119873
119895or not according to
probability theory the probability that grids 119866119894are sensed by
at least one node is
119901119892(119866119894) = 1 minus
119860119899
prod
119895=1
(1 minus 119901119892119899
(119866119894 119873119895)) (6)
In this paper the probability that all center points of grids119866119894in monitor area are sensed by at least one node is
approximated to network coverage ratio 120578
120578 =
sum119860119892
119894=1119901119892(119866119894)
119860119892
(7)
3 Particle Swarm Optimization Algorithm
The network coverage problem can be abstracted as theoptimization goal of the network coverage and the non-constrained optimization problem of the decision variablesis based on the coordinate of the node In this paper theparticle swarm optimization algorithm is used to solve theoptimization problem Because the coordinate value of thedecision variable node is continuous it is different fromthe task assignment problem and the network coverageproblem needs the continuous particle swarm optimizationalgorithm Since the particle swarm optimization algorithmhas been proposed many researchers have put forward manyimproved algorithms based on different practical applica-tions
31 Basic Particle Swarm Optimization Algorithm Particleswarm optimization algorithm is designed from research onbird flock preying behavior Assuming that there is onlyone piece of food in a searching area and that bird flock israndomly distributed in this area without knowing where thefood is and how far away from its location its task is to findthat food Each individual in the bird flock updates its currentposition according to history information of individual aswell as group By updating location constantly the bird flockconfirms the exact location of food thus completing preyingtask The researcher is inspired by bird flock preying modelhence particle swarm optimization algorithm is proposed to
4 Journal of Sensors
solve optimization problem There are solutions in researcharea wherein particle swarm is randomly located in and eachparticle is a potential solution to optimization problemTheseparticles are evaluated by fitness value which is decided byoptimization target function and each particle decides itsownflying speed information according to history best fitnessvalue of its own as well as group and then moves at this speedin entire solution space that is the individual exchangesinformation with other particles in some certain forms to getheuristic information to lead groupmovement hence gettingoptimum solution to optimization problem
Mathematical description on basic PSO algorithm is asfollows
Assuming that population size of particle swarm is 119899decision space is119898 wherein the location of particle 119868 at time119905 denotes119883(119905)
119894= (119909(119905)
1198941 119909(119905)
1198942 119909
(119905)
119894119898) 119894 = 1 2 119899 and speed
of particle 119868 is defined as particle moving distance in eachiteration which is denoted as 119881(119905)
119894= (V(119905)1198941 V(119905)1198942 V(119905)
119894119898) 119894 =
1 2 119899 hence the moving speed and location of particle 119868at time 119905 + 1 in 119889 (119889 = 1 2 119898) space change according tothe formulas below [10]
V(119905+1)119894119889
= 119908 sdot V(119905)119894119889
+ 1198881sdot 1199031sdot (119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032
sdot (119892(119905)
119889minus 119909(119905)
119894119889)
(8)
V(119905+1)119894119889
=
Vmax V(119905+1)119894119889
gt Vmax
minusVmax V(119905+1)119894119889
lt minusVmax(9)
119909(119905+1)
119894119889= 119909(119905)
119894119889+ V(119905+1)119894119889
(10)
wherein in formula (8) 119908 is for inertia weight whichis mainly for producing disturbance to prevent prematureconvergence on algorithm 119888
1and 1198882are for acceleration con-
stants which adjust maximum step size of particle moving tothe best individual particle and the best global particle and 119903
1
and 1199032are two randomnumbers in range [0 1] 119901(119905)
119894119889is for 119889th-
dimensional component of individual extremum 119901best 119892(119905)
119889
is for 119889th-dimensional component of global extremum 119892bestIn formula (9) Vmax is for particle max flight speed whichis a constant and is used to limit particle max flight speedto improve searching result As shown in formulas (8)sim(10)particle moving velocity increment is closely related to itsown history flying experience and group flying experienceand limited by max flight speed [11]
32 Particle SwarmOptimization Algorithmwith CompressionFactor Learning factors 119888
1and 1198882and the particles having a
self-summary to the group of outstanding individual learningability respectively this reflects the exchange of informationbetween the particle swarm If 119888
1is larger the particle will
make more wandering in the local area and if 1198882is larger the
particle will prematurely be converged as a local minimumvalue
In order to control the particle speed effectively makingthe algorithm balanced between global and local optimiza-tion Clerc and Kennedy [12] proposed a constriction factor
PSO algorithm and the speed of the particle update formulawill be changed
V(119905+1)119894119889
= 120593
sdot V(119905)119894119889
+ 1198881sdot 1199031(119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032(119892(119905)
119889minus 119909(119905)
119894119889)
120593 =2
100381610038161003816100381610038162 minus 119862radic1198622 minus 4119862
10038161003816100381610038161003816
119862 = 1198881+ 1198882
(11)
In order to ensure the solution of the algorithm 1198881+
1198882value must be greater than 4 Typical parameters are as
follows
(1) 1198881= 1198882= 205 119862 = 41 and shrinkage factor 120593 is
0729
(2) Particle population size pop = 30 1198881= 28 119888
2= 13 119862
is 41 at this time and the shrinkage factor 120593 is 0729
33 Particle Swarm Optimization Algorithm with ImprovedWeight Inertia weight 119908 is one of the most importantparameters in PSO the global search ability of the algorithmwill be improved with the help of the larger 119908 value and asmall119908 value is to enhance the capacity of local optimizationalgorithm According to different weights 119908 can be dividedinto PSO linearly decreasing weights by adaptive weightmethod and random weight method [13]
Linearly Decreasing Weights [14] Let inertia weight decreaselinearly from the maximum value 119908max to 119908min at thebeginning a larger 119908 value is to optimum algorithm out oflocal conductively and the latter algorithm is in favor of localspace for precise search Inertia weight 119908 relationship withthe number is
119908 = 119908max minus119905 lowast (119908max minus 119908min)
119905max (12)
where 119908max and 119908min denote the inertia weight maximumand minimum values 119905 represents the current numberof iterations and 119905max is the maximum number of itera-tions
Adaptive weight method is that the inertia weight 119908 withthe fitness value of particles is automatically changed Thismethod takes into account the particle current fitness value119891 and the relationship between the average fitness value 119891averand the minimum fitness value 119891min in all particles Whenthe fitness value of all the particles tends to converge or beoptimum the inertia weight 119908 is greater when the fitnessvalue of all the particles scattered inertia weight 119908 takes asmaller value Meanwhile when the fitness value of particlesis better than average fitness value 119891aver this corresponds toa smaller inertia weight when the fitness value of particlesis worse than average fitness value 119891aver this corresponds to
Journal of Sensors 5
a larger inertia weight so that the particles move closer tobetter search area Inertia weight 119908 is expressed as
119908
=
119908max minus(119908max minus 119908min) lowast (119891 minus 119891min)
(119891avg minus 119891min) 119891 le 119891avg
119908max 119891 gt 119891avg
(13)
Random weight method [15] is that the inertia weight 119908obeys a certain random number distributed randomly If atthe beginning of the algorithm the particle position is closeto the best point linearly decreasing the weight of the larger119908 values may deviate from the optimum region and randomweights 119908 may have a relatively small value accelerating theconvergence speed If at the beginning of the algorithm theparticles could not be found in the optimum area the weights119908 method is decreased linearly because of diminishing soultimately the algorithm cannot be converged to the bestadvantage and the randomweightmethod can overcome thislimitation Therefore in practical problems some randomweighting method can get better results than linear declinelaw Inertia weight 119908 is expressed as
119908 = 120583 + 120590 sdot 119873 (0 1)
120583 = 120583min + (120583max minus 120583min) lowast rand(14)
wherein 120583 represents a random weighted mean 120583max and120583min respectively and the minimum and maximum ran-dom weights mean 120590 represents a random weights vari-ance 119873(0 1) represents the standard normal distribution ofrandom numbers and rand represents a random numberbetween 0 and 1
34 Particle Swarm Optimization Algorithm with ImprovedLearning Factor In the practical application of the algorithmthe value of learning the way factor is 119888
1= 1198882= 2 there are
other variable learning factors a common synchronous andasynchronous learning factor is changed
Synchronous learning factor that is changed by 1198881and 1198882
at the same time decreasing linearly their relationship with 119905
is as follows
1198881= 1198882= 119888max minus
119888max minus 119888min119905max
sdot 119905 (15)
where 119888max and 119888min are themaximumandminimum learningfactors usually the maximum value is 21 and the minimumis 08
Asynchronous learning factor changes [16] are 1198881and 1198882
having various changes over time Larger initial algorithmis 1198881 1198882is smaller so that the particles have a greater
self-learning ability and smaller social learning ability theparticles can search the entire search space globally Latersmaller algorithm 119888
1 1198882has larger particles having a smaller
self-learning ability and greater social learning ability the
particles can accurately search the optimum area Learningfactor is expressed in as
1198881= 119888max minus
119888max minus 119888min119905max
sdot 119905
1198882= 119888min +
119888max minus 119888min119905max
sdot 119905
(16)
Ratnaweera et al [17] found experimentally that in mostcases 119888max = 25 119888min = 05 can be taken to achieve the idealsolution
35 Hybrid Particle Swarm Optimization In addition toswarm intelligence algorithm and particle swarm opti-mization algorithm but also including genetic algorithmssimulated annealing algorithm and firefly algorithm eachalgorithm has its unique advantages Hybrid particle swarmoptimization refers to the other intelligent optimizationalgorithms into the ideological hybrid algorithm particleswarm optimization algorithm formation
The genetic algorithm and particle swarm optimizationalgorithm combined GA-PSO algorithm is proposed byPremalatha and Natarajan [18] The genetic algorithm ofnatural selection mechanism (Selection) applied to PSOthe basic idea is that in each iteration all the particles aresorted according to their fitness values and a good half ofthe particles are of fitness location and speed value ratherthan another half that are sorted according to the positionand velocity of a particle while maintaining all particlesfitness unchanged By eliminating the difference betweenthe particles the algorithm can achieve faster convergenceHybrid genetic algorithm mechanism (crossover) applied toPSO is that in each iteration randomly select a fixed numberof particles into the hybrid cell the particles cross the poolpairwise hybridization to give the same number of progenyparticles with particle replacing the parent progeny particlesiteration populationWherein the position and velocity of theparticle and offspring (18) is determined by formula (17)
119909child = 119901 sdot 119909parent1 + (1 minus 119901) sdot 119909parent2 (17)
Vchild =
Vparent1 + Vparent210038161003816100381610038161003816Vparent1 + Vparent2
10038161003816100381610038161003816
sdot10038161003816100381610038161003816Vparent
10038161003816100381610038161003816 (18)
wherein119901 is a randomnumber [0 1] and Vparent can be chosenrandomly as Vparent1 or Vparent2 By hybridization technologyit can improve particle swarm diversity avoiding prematureconvergence algorithm
Liu et al [19] proposed the chaotic particle swarm opti-mization algorithm in order to optimize the particle swarmoptimization algorithm Chaos (chaos) is a nonlinear phe-nomenon in nature in a ubiquitous periodicity randomnessand intrinsic regularity Periodicity of chaos embodied in itcannot be repeated through all the states in a search spacerandomness is reflected in its performance similar to messyrandom variable which embodies the inherent regularity innonlinear systems under certain conditions defined in it Inaddition the chaotic initial conditions that are particularlysensitive to the initial value of the extremely weak changes
6 Journal of Sensors
will cause a huge deviation in the system Because chaos iseasy to implement andmake the algorithmout of local optimaspecial properties the researchers propose a chaotic opti-mization idea Periodicity of chaos randomness and chaosinherent regularity of such thinking can be complementaryoptimization algorithm combined with PSO
Victoire and Jeyakumar [20] proposed PSO and sequen-tial quadratic programming (SQP) method for solving thecombined economic dispatch (economic dispatch problemEDP) SQP is a nonlinear programming method it startsfrom a single point of search and uses gradient informationobtained final solution Research by three different EDPquestions the validity of the method
Lu et al [21] have introduced the real value of themutation operator (real-valued mutation RVM) into theparticle swarm optimization algorithm the algorithm is usedto improve the global search ability Interestingly whenthe RVM operator is applied to different functions it canbe operated effectively By comparing the experiments theauthors found that a combination of shrinkage factor inertiaweight and RVM operator mixed CBPSO-RVM algorithmcan perform better in most of the test cases
4 Particle Swarm Optimization AlgorithmFused with Idea from Simulated Annealing
Particle swarm optimization algorithm can be easily trappedin the local optimum and result in premature convergenceProbabilistic jumping property of simulated annealing SAmakes it possible to complementary associate with particleswarm optimization algorithm and fuses PSO global explo-ration capacity with SA local exploration capacity
Annealing in metallurgy refers to heating and thencooling the material at a specific rate which is for increasingthe volume of crystal grains and reducing defects in thecrystal lattice At the beginning material atom is at a positionwhich has local minimum internal energy then heatingincreases atoms energy and atoms leave the initial positionand move randomly to other locations When annealingcools down atoms are with low speed so it is possiblefor atoms to find a location with lower internal energythan initial ones Inspired by annealing of metals researcherproposes simulated annealing to solve optimization prob-lem Optimization problem searches every potential solutionto represent atoms location and evaluation function forpotential solution represents atoms internal energy at currentlocation wherein the optimization purpose is to find anoptimization solution hence getting a minimum value forevaluation function of this solution
Simulated annealing is with mutation probability insearching process which can effectively avoid the algorithmbeing trapped in the local optimum in iteration process Thekey to this algorithm is to refuse local minimum solution incertain probability and then skip over local minimum pointand continue to search other possible solutions in search areaalso the probability decreases along with temperature
This paper fuses particle swarm optimization algorithmand simulated annealing to solve coverage restoring problem
in wireless sensor actuator network Algorithm detailed stepsare as below
Step 1 Initialize basic parameters like population size themaximum number of iterations inertia weight learning fac-tor annealing constant and so on Set upper as well as lowerbounds for particle location and particle speed Initialize eachparticle location in swarm as all nodes coordinate in networkwith coverage and randomly initialize each particle speed
Step 2 Calculate fitness value 119891(119901119894) of each particle 119901
119894 Take
current location and fitness value of each particle as its historybest location and fitness value 119901best Use location of particle119901119892with best fitness value as swarm history best location and
corresponding best fitness value 119891(119901119892) as swarm best fitness
value
Step 3 Determine initial temperature according to the for-mula
1198790=
119891 (119901119892)
ln 5 (19)
Step 4 According to fitness value 119891(119901119894) and global best value
119891(119901119892) of each particle119901
119894 calculate fitted value of each particle
fitness value under current temperature
TF (119901119894) =
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
sumpop119894=1
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
(20)
Step 5 According to fitted value of each particle fitness valuefuse with roulette strategy and confirm replacement value119901119903
119892of global optimal particle 119901
119892from all particles Then
substitute fitted value into particle moving update equationto solve particle new speed and new location for applying innext iteration
Step 6 Calculate fitness value of each particle and updateparticles 119901best and swarm 119892best
Step 7 Operate annealing according to formula (21) wherein120582 is for annealing constant and 119896 is for iterative times
119879119896+1
= 120582 sdot 119879119896 (21)
Step 8 If the algorithm reaches either predicted operationalprecision or max iterative times then algorithm ends Orreturn to Step 4
5 Simulation Experiment
51 Particle Parameter Description Coverage restoring prob-lem can be abstracted into nonconstrained optimizationproblem which takes network coverage ratio as optimiza-tion target and nodes coordinates as decision variable Thischapter describes particle parameter Particle location X isfor all nodes coordinates which can be expressed as X =
1199091 1199101 1199092 1199102 119909
119894 119910119894 119909
119873 119910119873 wherein 119873 is for nodes
number and 119909119894 119910119894(1 le 119894 le 119873) are for abscissa and ordinate of
Journal of Sensors 7
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
1527
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 3 The initial deployment of nodes
particle 119894 Monitor area is a square two-dimensional regionwherein origin of coordinate is square vertex at the lowerleft corner so both abscissa and ordinate of particle satisfy0 le 119909119894 119910119894le 119871 wherein 119871 is for side length of monitor area
Particle velocity V is for incremental of particle locationand can be expressed as V = V
1199091 V1199101 V1199092 V1199102 V
119909119894
V119910119894 V
119909119899 V119910119899 wherein each dimension element value of
velocity is corresponding to each dimension element valueof position and indicates corresponding coordinate valueschange To limit particle velocity upper Vmax and lower Vminbounds of particle velocity need to be set
Particle fitness value function is reciprocal value ofnetwork coverage based on gridswhich arementioned in Sec-tion 22 as shown in formula (22) So algorithm solving targetis network nodes coordinate distributionwhichminimize thefitness function value
min fitness = 1
120578=
119860119892
sum119860119892
119894=1119901119892(119866119894)
(22)
52 Experiment Result andAnalysis In this paper the solvingmethod for coverage restoring problem is simulated inMAT-LAB 2012a as experimental environment Nodes number119873 =
100 and monitor area side length 119871 = 500m nodes sensingradius 119877
119904= 30m nodes possibility sensing model parameter
119903 = 6m 120582 = 120573 = 05 and grids number 119860119892= 100 During
initialization nodes are deployed randomly and evenly inwhole monitor area and initial deployment of nodes is asshown in Figure 3 In this figure every dot is for nodesnumber beside is for node number and circle region is fornodes sensing region As shown in the figure there are 4obvious holes in initial deployment of nodes and the solvingtarget of network coverage problem is to move redundantnodes beside holes hence increasing network coverage
To verify effectiveness of particle swarm optimizationalgorithm which is based on simulated annealing this paperuses basic particle swarmoptimization algorithm and variousimproved algorithms to simulate and compare on network
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
5001
2
3
4
56
7
8
9 10
11
12
13
14
15
1617
18
193191
20
21
22
23
24
25
26
27
28
29
30
32
33
34
3536
3738
39
40
41
42
43
44
45
46
47
48
49
50
52
5354
5557
5158
59
60
61
62
63
64
65
66
67
68
69
70
7172
73
74
75
5676
77
78
79
80
8182
83
84
85
86
87
88
89
90
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 4 The final deployment of nodes (BPSO)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
921527
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 5 The final deployment of nodes (GPSOmdashcrossover)
coverage problem Figures 4ndash7 are the final deployments ofnodes which are simulated from basic particle swarm opti-mization algorithm particle swarm optimization algorithmfused with crossover mutation idea from genetic algorithmparticle swarm optimization algorithm based on simulatedannealing and with compression factor and particle swarmoptimization algorithm based on simulated annealing andusing asynchronous learning factors Figure 8 is comparisonon best fitness value change in iteration process of eachalgorithm
After analyzing simulation results from each algorithmwe can see that simulation effect fromGPSO is the worst andSAPSOwith compression factor is the bestThe final purposeof particle movement is to improve network coverage bymoving redundant node and restoring network holes atthe meantime to avoid too much energy consumptionmoving distance of redundant node cannot be too far Ineach algorithm the nodes moving distance is controlled byparticle upper Vmax and lower Vmin bounds According to
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
45
46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
23
24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
43
44
45
46
47
48
50
51
52
5354 55
56
57
58
59
60
61
62
64
65
66
67
68
6971
72
7374
75
76
77
7899
79
80
8182
83
84
85
86
87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
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International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
4 Journal of Sensors
solve optimization problem There are solutions in researcharea wherein particle swarm is randomly located in and eachparticle is a potential solution to optimization problemTheseparticles are evaluated by fitness value which is decided byoptimization target function and each particle decides itsownflying speed information according to history best fitnessvalue of its own as well as group and then moves at this speedin entire solution space that is the individual exchangesinformation with other particles in some certain forms to getheuristic information to lead groupmovement hence gettingoptimum solution to optimization problem
Mathematical description on basic PSO algorithm is asfollows
Assuming that population size of particle swarm is 119899decision space is119898 wherein the location of particle 119868 at time119905 denotes119883(119905)
119894= (119909(119905)
1198941 119909(119905)
1198942 119909
(119905)
119894119898) 119894 = 1 2 119899 and speed
of particle 119868 is defined as particle moving distance in eachiteration which is denoted as 119881(119905)
119894= (V(119905)1198941 V(119905)1198942 V(119905)
119894119898) 119894 =
1 2 119899 hence the moving speed and location of particle 119868at time 119905 + 1 in 119889 (119889 = 1 2 119898) space change according tothe formulas below [10]
V(119905+1)119894119889
= 119908 sdot V(119905)119894119889
+ 1198881sdot 1199031sdot (119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032
sdot (119892(119905)
119889minus 119909(119905)
119894119889)
(8)
V(119905+1)119894119889
=
Vmax V(119905+1)119894119889
gt Vmax
minusVmax V(119905+1)119894119889
lt minusVmax(9)
119909(119905+1)
119894119889= 119909(119905)
119894119889+ V(119905+1)119894119889
(10)
wherein in formula (8) 119908 is for inertia weight whichis mainly for producing disturbance to prevent prematureconvergence on algorithm 119888
1and 1198882are for acceleration con-
stants which adjust maximum step size of particle moving tothe best individual particle and the best global particle and 119903
1
and 1199032are two randomnumbers in range [0 1] 119901(119905)
119894119889is for 119889th-
dimensional component of individual extremum 119901best 119892(119905)
119889
is for 119889th-dimensional component of global extremum 119892bestIn formula (9) Vmax is for particle max flight speed whichis a constant and is used to limit particle max flight speedto improve searching result As shown in formulas (8)sim(10)particle moving velocity increment is closely related to itsown history flying experience and group flying experienceand limited by max flight speed [11]
32 Particle SwarmOptimization Algorithmwith CompressionFactor Learning factors 119888
1and 1198882and the particles having a
self-summary to the group of outstanding individual learningability respectively this reflects the exchange of informationbetween the particle swarm If 119888
1is larger the particle will
make more wandering in the local area and if 1198882is larger the
particle will prematurely be converged as a local minimumvalue
In order to control the particle speed effectively makingthe algorithm balanced between global and local optimiza-tion Clerc and Kennedy [12] proposed a constriction factor
PSO algorithm and the speed of the particle update formulawill be changed
V(119905+1)119894119889
= 120593
sdot V(119905)119894119889
+ 1198881sdot 1199031(119901(119905)
119894119889minus 119909(119905)
119894119889) + 1198882sdot 1199032(119892(119905)
119889minus 119909(119905)
119894119889)
120593 =2
100381610038161003816100381610038162 minus 119862radic1198622 minus 4119862
10038161003816100381610038161003816
119862 = 1198881+ 1198882
(11)
In order to ensure the solution of the algorithm 1198881+
1198882value must be greater than 4 Typical parameters are as
follows
(1) 1198881= 1198882= 205 119862 = 41 and shrinkage factor 120593 is
0729
(2) Particle population size pop = 30 1198881= 28 119888
2= 13 119862
is 41 at this time and the shrinkage factor 120593 is 0729
33 Particle Swarm Optimization Algorithm with ImprovedWeight Inertia weight 119908 is one of the most importantparameters in PSO the global search ability of the algorithmwill be improved with the help of the larger 119908 value and asmall119908 value is to enhance the capacity of local optimizationalgorithm According to different weights 119908 can be dividedinto PSO linearly decreasing weights by adaptive weightmethod and random weight method [13]
Linearly Decreasing Weights [14] Let inertia weight decreaselinearly from the maximum value 119908max to 119908min at thebeginning a larger 119908 value is to optimum algorithm out oflocal conductively and the latter algorithm is in favor of localspace for precise search Inertia weight 119908 relationship withthe number is
119908 = 119908max minus119905 lowast (119908max minus 119908min)
119905max (12)
where 119908max and 119908min denote the inertia weight maximumand minimum values 119905 represents the current numberof iterations and 119905max is the maximum number of itera-tions
Adaptive weight method is that the inertia weight 119908 withthe fitness value of particles is automatically changed Thismethod takes into account the particle current fitness value119891 and the relationship between the average fitness value 119891averand the minimum fitness value 119891min in all particles Whenthe fitness value of all the particles tends to converge or beoptimum the inertia weight 119908 is greater when the fitnessvalue of all the particles scattered inertia weight 119908 takes asmaller value Meanwhile when the fitness value of particlesis better than average fitness value 119891aver this corresponds toa smaller inertia weight when the fitness value of particlesis worse than average fitness value 119891aver this corresponds to
Journal of Sensors 5
a larger inertia weight so that the particles move closer tobetter search area Inertia weight 119908 is expressed as
119908
=
119908max minus(119908max minus 119908min) lowast (119891 minus 119891min)
(119891avg minus 119891min) 119891 le 119891avg
119908max 119891 gt 119891avg
(13)
Random weight method [15] is that the inertia weight 119908obeys a certain random number distributed randomly If atthe beginning of the algorithm the particle position is closeto the best point linearly decreasing the weight of the larger119908 values may deviate from the optimum region and randomweights 119908 may have a relatively small value accelerating theconvergence speed If at the beginning of the algorithm theparticles could not be found in the optimum area the weights119908 method is decreased linearly because of diminishing soultimately the algorithm cannot be converged to the bestadvantage and the randomweightmethod can overcome thislimitation Therefore in practical problems some randomweighting method can get better results than linear declinelaw Inertia weight 119908 is expressed as
119908 = 120583 + 120590 sdot 119873 (0 1)
120583 = 120583min + (120583max minus 120583min) lowast rand(14)
wherein 120583 represents a random weighted mean 120583max and120583min respectively and the minimum and maximum ran-dom weights mean 120590 represents a random weights vari-ance 119873(0 1) represents the standard normal distribution ofrandom numbers and rand represents a random numberbetween 0 and 1
34 Particle Swarm Optimization Algorithm with ImprovedLearning Factor In the practical application of the algorithmthe value of learning the way factor is 119888
1= 1198882= 2 there are
other variable learning factors a common synchronous andasynchronous learning factor is changed
Synchronous learning factor that is changed by 1198881and 1198882
at the same time decreasing linearly their relationship with 119905
is as follows
1198881= 1198882= 119888max minus
119888max minus 119888min119905max
sdot 119905 (15)
where 119888max and 119888min are themaximumandminimum learningfactors usually the maximum value is 21 and the minimumis 08
Asynchronous learning factor changes [16] are 1198881and 1198882
having various changes over time Larger initial algorithmis 1198881 1198882is smaller so that the particles have a greater
self-learning ability and smaller social learning ability theparticles can search the entire search space globally Latersmaller algorithm 119888
1 1198882has larger particles having a smaller
self-learning ability and greater social learning ability the
particles can accurately search the optimum area Learningfactor is expressed in as
1198881= 119888max minus
119888max minus 119888min119905max
sdot 119905
1198882= 119888min +
119888max minus 119888min119905max
sdot 119905
(16)
Ratnaweera et al [17] found experimentally that in mostcases 119888max = 25 119888min = 05 can be taken to achieve the idealsolution
35 Hybrid Particle Swarm Optimization In addition toswarm intelligence algorithm and particle swarm opti-mization algorithm but also including genetic algorithmssimulated annealing algorithm and firefly algorithm eachalgorithm has its unique advantages Hybrid particle swarmoptimization refers to the other intelligent optimizationalgorithms into the ideological hybrid algorithm particleswarm optimization algorithm formation
The genetic algorithm and particle swarm optimizationalgorithm combined GA-PSO algorithm is proposed byPremalatha and Natarajan [18] The genetic algorithm ofnatural selection mechanism (Selection) applied to PSOthe basic idea is that in each iteration all the particles aresorted according to their fitness values and a good half ofthe particles are of fitness location and speed value ratherthan another half that are sorted according to the positionand velocity of a particle while maintaining all particlesfitness unchanged By eliminating the difference betweenthe particles the algorithm can achieve faster convergenceHybrid genetic algorithm mechanism (crossover) applied toPSO is that in each iteration randomly select a fixed numberof particles into the hybrid cell the particles cross the poolpairwise hybridization to give the same number of progenyparticles with particle replacing the parent progeny particlesiteration populationWherein the position and velocity of theparticle and offspring (18) is determined by formula (17)
119909child = 119901 sdot 119909parent1 + (1 minus 119901) sdot 119909parent2 (17)
Vchild =
Vparent1 + Vparent210038161003816100381610038161003816Vparent1 + Vparent2
10038161003816100381610038161003816
sdot10038161003816100381610038161003816Vparent
10038161003816100381610038161003816 (18)
wherein119901 is a randomnumber [0 1] and Vparent can be chosenrandomly as Vparent1 or Vparent2 By hybridization technologyit can improve particle swarm diversity avoiding prematureconvergence algorithm
Liu et al [19] proposed the chaotic particle swarm opti-mization algorithm in order to optimize the particle swarmoptimization algorithm Chaos (chaos) is a nonlinear phe-nomenon in nature in a ubiquitous periodicity randomnessand intrinsic regularity Periodicity of chaos embodied in itcannot be repeated through all the states in a search spacerandomness is reflected in its performance similar to messyrandom variable which embodies the inherent regularity innonlinear systems under certain conditions defined in it Inaddition the chaotic initial conditions that are particularlysensitive to the initial value of the extremely weak changes
6 Journal of Sensors
will cause a huge deviation in the system Because chaos iseasy to implement andmake the algorithmout of local optimaspecial properties the researchers propose a chaotic opti-mization idea Periodicity of chaos randomness and chaosinherent regularity of such thinking can be complementaryoptimization algorithm combined with PSO
Victoire and Jeyakumar [20] proposed PSO and sequen-tial quadratic programming (SQP) method for solving thecombined economic dispatch (economic dispatch problemEDP) SQP is a nonlinear programming method it startsfrom a single point of search and uses gradient informationobtained final solution Research by three different EDPquestions the validity of the method
Lu et al [21] have introduced the real value of themutation operator (real-valued mutation RVM) into theparticle swarm optimization algorithm the algorithm is usedto improve the global search ability Interestingly whenthe RVM operator is applied to different functions it canbe operated effectively By comparing the experiments theauthors found that a combination of shrinkage factor inertiaweight and RVM operator mixed CBPSO-RVM algorithmcan perform better in most of the test cases
4 Particle Swarm Optimization AlgorithmFused with Idea from Simulated Annealing
Particle swarm optimization algorithm can be easily trappedin the local optimum and result in premature convergenceProbabilistic jumping property of simulated annealing SAmakes it possible to complementary associate with particleswarm optimization algorithm and fuses PSO global explo-ration capacity with SA local exploration capacity
Annealing in metallurgy refers to heating and thencooling the material at a specific rate which is for increasingthe volume of crystal grains and reducing defects in thecrystal lattice At the beginning material atom is at a positionwhich has local minimum internal energy then heatingincreases atoms energy and atoms leave the initial positionand move randomly to other locations When annealingcools down atoms are with low speed so it is possiblefor atoms to find a location with lower internal energythan initial ones Inspired by annealing of metals researcherproposes simulated annealing to solve optimization prob-lem Optimization problem searches every potential solutionto represent atoms location and evaluation function forpotential solution represents atoms internal energy at currentlocation wherein the optimization purpose is to find anoptimization solution hence getting a minimum value forevaluation function of this solution
Simulated annealing is with mutation probability insearching process which can effectively avoid the algorithmbeing trapped in the local optimum in iteration process Thekey to this algorithm is to refuse local minimum solution incertain probability and then skip over local minimum pointand continue to search other possible solutions in search areaalso the probability decreases along with temperature
This paper fuses particle swarm optimization algorithmand simulated annealing to solve coverage restoring problem
in wireless sensor actuator network Algorithm detailed stepsare as below
Step 1 Initialize basic parameters like population size themaximum number of iterations inertia weight learning fac-tor annealing constant and so on Set upper as well as lowerbounds for particle location and particle speed Initialize eachparticle location in swarm as all nodes coordinate in networkwith coverage and randomly initialize each particle speed
Step 2 Calculate fitness value 119891(119901119894) of each particle 119901
119894 Take
current location and fitness value of each particle as its historybest location and fitness value 119901best Use location of particle119901119892with best fitness value as swarm history best location and
corresponding best fitness value 119891(119901119892) as swarm best fitness
value
Step 3 Determine initial temperature according to the for-mula
1198790=
119891 (119901119892)
ln 5 (19)
Step 4 According to fitness value 119891(119901119894) and global best value
119891(119901119892) of each particle119901
119894 calculate fitted value of each particle
fitness value under current temperature
TF (119901119894) =
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
sumpop119894=1
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
(20)
Step 5 According to fitted value of each particle fitness valuefuse with roulette strategy and confirm replacement value119901119903
119892of global optimal particle 119901
119892from all particles Then
substitute fitted value into particle moving update equationto solve particle new speed and new location for applying innext iteration
Step 6 Calculate fitness value of each particle and updateparticles 119901best and swarm 119892best
Step 7 Operate annealing according to formula (21) wherein120582 is for annealing constant and 119896 is for iterative times
119879119896+1
= 120582 sdot 119879119896 (21)
Step 8 If the algorithm reaches either predicted operationalprecision or max iterative times then algorithm ends Orreturn to Step 4
5 Simulation Experiment
51 Particle Parameter Description Coverage restoring prob-lem can be abstracted into nonconstrained optimizationproblem which takes network coverage ratio as optimiza-tion target and nodes coordinates as decision variable Thischapter describes particle parameter Particle location X isfor all nodes coordinates which can be expressed as X =
1199091 1199101 1199092 1199102 119909
119894 119910119894 119909
119873 119910119873 wherein 119873 is for nodes
number and 119909119894 119910119894(1 le 119894 le 119873) are for abscissa and ordinate of
Journal of Sensors 7
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
1527
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 3 The initial deployment of nodes
particle 119894 Monitor area is a square two-dimensional regionwherein origin of coordinate is square vertex at the lowerleft corner so both abscissa and ordinate of particle satisfy0 le 119909119894 119910119894le 119871 wherein 119871 is for side length of monitor area
Particle velocity V is for incremental of particle locationand can be expressed as V = V
1199091 V1199101 V1199092 V1199102 V
119909119894
V119910119894 V
119909119899 V119910119899 wherein each dimension element value of
velocity is corresponding to each dimension element valueof position and indicates corresponding coordinate valueschange To limit particle velocity upper Vmax and lower Vminbounds of particle velocity need to be set
Particle fitness value function is reciprocal value ofnetwork coverage based on gridswhich arementioned in Sec-tion 22 as shown in formula (22) So algorithm solving targetis network nodes coordinate distributionwhichminimize thefitness function value
min fitness = 1
120578=
119860119892
sum119860119892
119894=1119901119892(119866119894)
(22)
52 Experiment Result andAnalysis In this paper the solvingmethod for coverage restoring problem is simulated inMAT-LAB 2012a as experimental environment Nodes number119873 =
100 and monitor area side length 119871 = 500m nodes sensingradius 119877
119904= 30m nodes possibility sensing model parameter
119903 = 6m 120582 = 120573 = 05 and grids number 119860119892= 100 During
initialization nodes are deployed randomly and evenly inwhole monitor area and initial deployment of nodes is asshown in Figure 3 In this figure every dot is for nodesnumber beside is for node number and circle region is fornodes sensing region As shown in the figure there are 4obvious holes in initial deployment of nodes and the solvingtarget of network coverage problem is to move redundantnodes beside holes hence increasing network coverage
To verify effectiveness of particle swarm optimizationalgorithm which is based on simulated annealing this paperuses basic particle swarmoptimization algorithm and variousimproved algorithms to simulate and compare on network
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
5001
2
3
4
56
7
8
9 10
11
12
13
14
15
1617
18
193191
20
21
22
23
24
25
26
27
28
29
30
32
33
34
3536
3738
39
40
41
42
43
44
45
46
47
48
49
50
52
5354
5557
5158
59
60
61
62
63
64
65
66
67
68
69
70
7172
73
74
75
5676
77
78
79
80
8182
83
84
85
86
87
88
89
90
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 4 The final deployment of nodes (BPSO)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
921527
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 5 The final deployment of nodes (GPSOmdashcrossover)
coverage problem Figures 4ndash7 are the final deployments ofnodes which are simulated from basic particle swarm opti-mization algorithm particle swarm optimization algorithmfused with crossover mutation idea from genetic algorithmparticle swarm optimization algorithm based on simulatedannealing and with compression factor and particle swarmoptimization algorithm based on simulated annealing andusing asynchronous learning factors Figure 8 is comparisonon best fitness value change in iteration process of eachalgorithm
After analyzing simulation results from each algorithmwe can see that simulation effect fromGPSO is the worst andSAPSOwith compression factor is the bestThe final purposeof particle movement is to improve network coverage bymoving redundant node and restoring network holes atthe meantime to avoid too much energy consumptionmoving distance of redundant node cannot be too far Ineach algorithm the nodes moving distance is controlled byparticle upper Vmax and lower Vmin bounds According to
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
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46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
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24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
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52
5354 55
56
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6971
72
7374
75
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77
7899
79
80
8182
83
84
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87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Sensors 5
a larger inertia weight so that the particles move closer tobetter search area Inertia weight 119908 is expressed as
119908
=
119908max minus(119908max minus 119908min) lowast (119891 minus 119891min)
(119891avg minus 119891min) 119891 le 119891avg
119908max 119891 gt 119891avg
(13)
Random weight method [15] is that the inertia weight 119908obeys a certain random number distributed randomly If atthe beginning of the algorithm the particle position is closeto the best point linearly decreasing the weight of the larger119908 values may deviate from the optimum region and randomweights 119908 may have a relatively small value accelerating theconvergence speed If at the beginning of the algorithm theparticles could not be found in the optimum area the weights119908 method is decreased linearly because of diminishing soultimately the algorithm cannot be converged to the bestadvantage and the randomweightmethod can overcome thislimitation Therefore in practical problems some randomweighting method can get better results than linear declinelaw Inertia weight 119908 is expressed as
119908 = 120583 + 120590 sdot 119873 (0 1)
120583 = 120583min + (120583max minus 120583min) lowast rand(14)
wherein 120583 represents a random weighted mean 120583max and120583min respectively and the minimum and maximum ran-dom weights mean 120590 represents a random weights vari-ance 119873(0 1) represents the standard normal distribution ofrandom numbers and rand represents a random numberbetween 0 and 1
34 Particle Swarm Optimization Algorithm with ImprovedLearning Factor In the practical application of the algorithmthe value of learning the way factor is 119888
1= 1198882= 2 there are
other variable learning factors a common synchronous andasynchronous learning factor is changed
Synchronous learning factor that is changed by 1198881and 1198882
at the same time decreasing linearly their relationship with 119905
is as follows
1198881= 1198882= 119888max minus
119888max minus 119888min119905max
sdot 119905 (15)
where 119888max and 119888min are themaximumandminimum learningfactors usually the maximum value is 21 and the minimumis 08
Asynchronous learning factor changes [16] are 1198881and 1198882
having various changes over time Larger initial algorithmis 1198881 1198882is smaller so that the particles have a greater
self-learning ability and smaller social learning ability theparticles can search the entire search space globally Latersmaller algorithm 119888
1 1198882has larger particles having a smaller
self-learning ability and greater social learning ability the
particles can accurately search the optimum area Learningfactor is expressed in as
1198881= 119888max minus
119888max minus 119888min119905max
sdot 119905
1198882= 119888min +
119888max minus 119888min119905max
sdot 119905
(16)
Ratnaweera et al [17] found experimentally that in mostcases 119888max = 25 119888min = 05 can be taken to achieve the idealsolution
35 Hybrid Particle Swarm Optimization In addition toswarm intelligence algorithm and particle swarm opti-mization algorithm but also including genetic algorithmssimulated annealing algorithm and firefly algorithm eachalgorithm has its unique advantages Hybrid particle swarmoptimization refers to the other intelligent optimizationalgorithms into the ideological hybrid algorithm particleswarm optimization algorithm formation
The genetic algorithm and particle swarm optimizationalgorithm combined GA-PSO algorithm is proposed byPremalatha and Natarajan [18] The genetic algorithm ofnatural selection mechanism (Selection) applied to PSOthe basic idea is that in each iteration all the particles aresorted according to their fitness values and a good half ofthe particles are of fitness location and speed value ratherthan another half that are sorted according to the positionand velocity of a particle while maintaining all particlesfitness unchanged By eliminating the difference betweenthe particles the algorithm can achieve faster convergenceHybrid genetic algorithm mechanism (crossover) applied toPSO is that in each iteration randomly select a fixed numberof particles into the hybrid cell the particles cross the poolpairwise hybridization to give the same number of progenyparticles with particle replacing the parent progeny particlesiteration populationWherein the position and velocity of theparticle and offspring (18) is determined by formula (17)
119909child = 119901 sdot 119909parent1 + (1 minus 119901) sdot 119909parent2 (17)
Vchild =
Vparent1 + Vparent210038161003816100381610038161003816Vparent1 + Vparent2
10038161003816100381610038161003816
sdot10038161003816100381610038161003816Vparent
10038161003816100381610038161003816 (18)
wherein119901 is a randomnumber [0 1] and Vparent can be chosenrandomly as Vparent1 or Vparent2 By hybridization technologyit can improve particle swarm diversity avoiding prematureconvergence algorithm
Liu et al [19] proposed the chaotic particle swarm opti-mization algorithm in order to optimize the particle swarmoptimization algorithm Chaos (chaos) is a nonlinear phe-nomenon in nature in a ubiquitous periodicity randomnessand intrinsic regularity Periodicity of chaos embodied in itcannot be repeated through all the states in a search spacerandomness is reflected in its performance similar to messyrandom variable which embodies the inherent regularity innonlinear systems under certain conditions defined in it Inaddition the chaotic initial conditions that are particularlysensitive to the initial value of the extremely weak changes
6 Journal of Sensors
will cause a huge deviation in the system Because chaos iseasy to implement andmake the algorithmout of local optimaspecial properties the researchers propose a chaotic opti-mization idea Periodicity of chaos randomness and chaosinherent regularity of such thinking can be complementaryoptimization algorithm combined with PSO
Victoire and Jeyakumar [20] proposed PSO and sequen-tial quadratic programming (SQP) method for solving thecombined economic dispatch (economic dispatch problemEDP) SQP is a nonlinear programming method it startsfrom a single point of search and uses gradient informationobtained final solution Research by three different EDPquestions the validity of the method
Lu et al [21] have introduced the real value of themutation operator (real-valued mutation RVM) into theparticle swarm optimization algorithm the algorithm is usedto improve the global search ability Interestingly whenthe RVM operator is applied to different functions it canbe operated effectively By comparing the experiments theauthors found that a combination of shrinkage factor inertiaweight and RVM operator mixed CBPSO-RVM algorithmcan perform better in most of the test cases
4 Particle Swarm Optimization AlgorithmFused with Idea from Simulated Annealing
Particle swarm optimization algorithm can be easily trappedin the local optimum and result in premature convergenceProbabilistic jumping property of simulated annealing SAmakes it possible to complementary associate with particleswarm optimization algorithm and fuses PSO global explo-ration capacity with SA local exploration capacity
Annealing in metallurgy refers to heating and thencooling the material at a specific rate which is for increasingthe volume of crystal grains and reducing defects in thecrystal lattice At the beginning material atom is at a positionwhich has local minimum internal energy then heatingincreases atoms energy and atoms leave the initial positionand move randomly to other locations When annealingcools down atoms are with low speed so it is possiblefor atoms to find a location with lower internal energythan initial ones Inspired by annealing of metals researcherproposes simulated annealing to solve optimization prob-lem Optimization problem searches every potential solutionto represent atoms location and evaluation function forpotential solution represents atoms internal energy at currentlocation wherein the optimization purpose is to find anoptimization solution hence getting a minimum value forevaluation function of this solution
Simulated annealing is with mutation probability insearching process which can effectively avoid the algorithmbeing trapped in the local optimum in iteration process Thekey to this algorithm is to refuse local minimum solution incertain probability and then skip over local minimum pointand continue to search other possible solutions in search areaalso the probability decreases along with temperature
This paper fuses particle swarm optimization algorithmand simulated annealing to solve coverage restoring problem
in wireless sensor actuator network Algorithm detailed stepsare as below
Step 1 Initialize basic parameters like population size themaximum number of iterations inertia weight learning fac-tor annealing constant and so on Set upper as well as lowerbounds for particle location and particle speed Initialize eachparticle location in swarm as all nodes coordinate in networkwith coverage and randomly initialize each particle speed
Step 2 Calculate fitness value 119891(119901119894) of each particle 119901
119894 Take
current location and fitness value of each particle as its historybest location and fitness value 119901best Use location of particle119901119892with best fitness value as swarm history best location and
corresponding best fitness value 119891(119901119892) as swarm best fitness
value
Step 3 Determine initial temperature according to the for-mula
1198790=
119891 (119901119892)
ln 5 (19)
Step 4 According to fitness value 119891(119901119894) and global best value
119891(119901119892) of each particle119901
119894 calculate fitted value of each particle
fitness value under current temperature
TF (119901119894) =
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
sumpop119894=1
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
(20)
Step 5 According to fitted value of each particle fitness valuefuse with roulette strategy and confirm replacement value119901119903
119892of global optimal particle 119901
119892from all particles Then
substitute fitted value into particle moving update equationto solve particle new speed and new location for applying innext iteration
Step 6 Calculate fitness value of each particle and updateparticles 119901best and swarm 119892best
Step 7 Operate annealing according to formula (21) wherein120582 is for annealing constant and 119896 is for iterative times
119879119896+1
= 120582 sdot 119879119896 (21)
Step 8 If the algorithm reaches either predicted operationalprecision or max iterative times then algorithm ends Orreturn to Step 4
5 Simulation Experiment
51 Particle Parameter Description Coverage restoring prob-lem can be abstracted into nonconstrained optimizationproblem which takes network coverage ratio as optimiza-tion target and nodes coordinates as decision variable Thischapter describes particle parameter Particle location X isfor all nodes coordinates which can be expressed as X =
1199091 1199101 1199092 1199102 119909
119894 119910119894 119909
119873 119910119873 wherein 119873 is for nodes
number and 119909119894 119910119894(1 le 119894 le 119873) are for abscissa and ordinate of
Journal of Sensors 7
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
1527
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 3 The initial deployment of nodes
particle 119894 Monitor area is a square two-dimensional regionwherein origin of coordinate is square vertex at the lowerleft corner so both abscissa and ordinate of particle satisfy0 le 119909119894 119910119894le 119871 wherein 119871 is for side length of monitor area
Particle velocity V is for incremental of particle locationand can be expressed as V = V
1199091 V1199101 V1199092 V1199102 V
119909119894
V119910119894 V
119909119899 V119910119899 wherein each dimension element value of
velocity is corresponding to each dimension element valueof position and indicates corresponding coordinate valueschange To limit particle velocity upper Vmax and lower Vminbounds of particle velocity need to be set
Particle fitness value function is reciprocal value ofnetwork coverage based on gridswhich arementioned in Sec-tion 22 as shown in formula (22) So algorithm solving targetis network nodes coordinate distributionwhichminimize thefitness function value
min fitness = 1
120578=
119860119892
sum119860119892
119894=1119901119892(119866119894)
(22)
52 Experiment Result andAnalysis In this paper the solvingmethod for coverage restoring problem is simulated inMAT-LAB 2012a as experimental environment Nodes number119873 =
100 and monitor area side length 119871 = 500m nodes sensingradius 119877
119904= 30m nodes possibility sensing model parameter
119903 = 6m 120582 = 120573 = 05 and grids number 119860119892= 100 During
initialization nodes are deployed randomly and evenly inwhole monitor area and initial deployment of nodes is asshown in Figure 3 In this figure every dot is for nodesnumber beside is for node number and circle region is fornodes sensing region As shown in the figure there are 4obvious holes in initial deployment of nodes and the solvingtarget of network coverage problem is to move redundantnodes beside holes hence increasing network coverage
To verify effectiveness of particle swarm optimizationalgorithm which is based on simulated annealing this paperuses basic particle swarmoptimization algorithm and variousimproved algorithms to simulate and compare on network
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
5001
2
3
4
56
7
8
9 10
11
12
13
14
15
1617
18
193191
20
21
22
23
24
25
26
27
28
29
30
32
33
34
3536
3738
39
40
41
42
43
44
45
46
47
48
49
50
52
5354
5557
5158
59
60
61
62
63
64
65
66
67
68
69
70
7172
73
74
75
5676
77
78
79
80
8182
83
84
85
86
87
88
89
90
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 4 The final deployment of nodes (BPSO)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
921527
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 5 The final deployment of nodes (GPSOmdashcrossover)
coverage problem Figures 4ndash7 are the final deployments ofnodes which are simulated from basic particle swarm opti-mization algorithm particle swarm optimization algorithmfused with crossover mutation idea from genetic algorithmparticle swarm optimization algorithm based on simulatedannealing and with compression factor and particle swarmoptimization algorithm based on simulated annealing andusing asynchronous learning factors Figure 8 is comparisonon best fitness value change in iteration process of eachalgorithm
After analyzing simulation results from each algorithmwe can see that simulation effect fromGPSO is the worst andSAPSOwith compression factor is the bestThe final purposeof particle movement is to improve network coverage bymoving redundant node and restoring network holes atthe meantime to avoid too much energy consumptionmoving distance of redundant node cannot be too far Ineach algorithm the nodes moving distance is controlled byparticle upper Vmax and lower Vmin bounds According to
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
45
46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
23
24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
43
44
45
46
47
48
50
51
52
5354 55
56
57
58
59
60
61
62
64
65
66
67
68
6971
72
7374
75
76
77
7899
79
80
8182
83
84
85
86
87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Journal of Sensors
will cause a huge deviation in the system Because chaos iseasy to implement andmake the algorithmout of local optimaspecial properties the researchers propose a chaotic opti-mization idea Periodicity of chaos randomness and chaosinherent regularity of such thinking can be complementaryoptimization algorithm combined with PSO
Victoire and Jeyakumar [20] proposed PSO and sequen-tial quadratic programming (SQP) method for solving thecombined economic dispatch (economic dispatch problemEDP) SQP is a nonlinear programming method it startsfrom a single point of search and uses gradient informationobtained final solution Research by three different EDPquestions the validity of the method
Lu et al [21] have introduced the real value of themutation operator (real-valued mutation RVM) into theparticle swarm optimization algorithm the algorithm is usedto improve the global search ability Interestingly whenthe RVM operator is applied to different functions it canbe operated effectively By comparing the experiments theauthors found that a combination of shrinkage factor inertiaweight and RVM operator mixed CBPSO-RVM algorithmcan perform better in most of the test cases
4 Particle Swarm Optimization AlgorithmFused with Idea from Simulated Annealing
Particle swarm optimization algorithm can be easily trappedin the local optimum and result in premature convergenceProbabilistic jumping property of simulated annealing SAmakes it possible to complementary associate with particleswarm optimization algorithm and fuses PSO global explo-ration capacity with SA local exploration capacity
Annealing in metallurgy refers to heating and thencooling the material at a specific rate which is for increasingthe volume of crystal grains and reducing defects in thecrystal lattice At the beginning material atom is at a positionwhich has local minimum internal energy then heatingincreases atoms energy and atoms leave the initial positionand move randomly to other locations When annealingcools down atoms are with low speed so it is possiblefor atoms to find a location with lower internal energythan initial ones Inspired by annealing of metals researcherproposes simulated annealing to solve optimization prob-lem Optimization problem searches every potential solutionto represent atoms location and evaluation function forpotential solution represents atoms internal energy at currentlocation wherein the optimization purpose is to find anoptimization solution hence getting a minimum value forevaluation function of this solution
Simulated annealing is with mutation probability insearching process which can effectively avoid the algorithmbeing trapped in the local optimum in iteration process Thekey to this algorithm is to refuse local minimum solution incertain probability and then skip over local minimum pointand continue to search other possible solutions in search areaalso the probability decreases along with temperature
This paper fuses particle swarm optimization algorithmand simulated annealing to solve coverage restoring problem
in wireless sensor actuator network Algorithm detailed stepsare as below
Step 1 Initialize basic parameters like population size themaximum number of iterations inertia weight learning fac-tor annealing constant and so on Set upper as well as lowerbounds for particle location and particle speed Initialize eachparticle location in swarm as all nodes coordinate in networkwith coverage and randomly initialize each particle speed
Step 2 Calculate fitness value 119891(119901119894) of each particle 119901
119894 Take
current location and fitness value of each particle as its historybest location and fitness value 119901best Use location of particle119901119892with best fitness value as swarm history best location and
corresponding best fitness value 119891(119901119892) as swarm best fitness
value
Step 3 Determine initial temperature according to the for-mula
1198790=
119891 (119901119892)
ln 5 (19)
Step 4 According to fitness value 119891(119901119894) and global best value
119891(119901119892) of each particle119901
119894 calculate fitted value of each particle
fitness value under current temperature
TF (119901119894) =
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
sumpop119894=1
exp (minus (119891 (119901119894) minus 119891 (119901
119892)) 119905)
(20)
Step 5 According to fitted value of each particle fitness valuefuse with roulette strategy and confirm replacement value119901119903
119892of global optimal particle 119901
119892from all particles Then
substitute fitted value into particle moving update equationto solve particle new speed and new location for applying innext iteration
Step 6 Calculate fitness value of each particle and updateparticles 119901best and swarm 119892best
Step 7 Operate annealing according to formula (21) wherein120582 is for annealing constant and 119896 is for iterative times
119879119896+1
= 120582 sdot 119879119896 (21)
Step 8 If the algorithm reaches either predicted operationalprecision or max iterative times then algorithm ends Orreturn to Step 4
5 Simulation Experiment
51 Particle Parameter Description Coverage restoring prob-lem can be abstracted into nonconstrained optimizationproblem which takes network coverage ratio as optimiza-tion target and nodes coordinates as decision variable Thischapter describes particle parameter Particle location X isfor all nodes coordinates which can be expressed as X =
1199091 1199101 1199092 1199102 119909
119894 119910119894 119909
119873 119910119873 wherein 119873 is for nodes
number and 119909119894 119910119894(1 le 119894 le 119873) are for abscissa and ordinate of
Journal of Sensors 7
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
1527
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 3 The initial deployment of nodes
particle 119894 Monitor area is a square two-dimensional regionwherein origin of coordinate is square vertex at the lowerleft corner so both abscissa and ordinate of particle satisfy0 le 119909119894 119910119894le 119871 wherein 119871 is for side length of monitor area
Particle velocity V is for incremental of particle locationand can be expressed as V = V
1199091 V1199101 V1199092 V1199102 V
119909119894
V119910119894 V
119909119899 V119910119899 wherein each dimension element value of
velocity is corresponding to each dimension element valueof position and indicates corresponding coordinate valueschange To limit particle velocity upper Vmax and lower Vminbounds of particle velocity need to be set
Particle fitness value function is reciprocal value ofnetwork coverage based on gridswhich arementioned in Sec-tion 22 as shown in formula (22) So algorithm solving targetis network nodes coordinate distributionwhichminimize thefitness function value
min fitness = 1
120578=
119860119892
sum119860119892
119894=1119901119892(119866119894)
(22)
52 Experiment Result andAnalysis In this paper the solvingmethod for coverage restoring problem is simulated inMAT-LAB 2012a as experimental environment Nodes number119873 =
100 and monitor area side length 119871 = 500m nodes sensingradius 119877
119904= 30m nodes possibility sensing model parameter
119903 = 6m 120582 = 120573 = 05 and grids number 119860119892= 100 During
initialization nodes are deployed randomly and evenly inwhole monitor area and initial deployment of nodes is asshown in Figure 3 In this figure every dot is for nodesnumber beside is for node number and circle region is fornodes sensing region As shown in the figure there are 4obvious holes in initial deployment of nodes and the solvingtarget of network coverage problem is to move redundantnodes beside holes hence increasing network coverage
To verify effectiveness of particle swarm optimizationalgorithm which is based on simulated annealing this paperuses basic particle swarmoptimization algorithm and variousimproved algorithms to simulate and compare on network
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
5001
2
3
4
56
7
8
9 10
11
12
13
14
15
1617
18
193191
20
21
22
23
24
25
26
27
28
29
30
32
33
34
3536
3738
39
40
41
42
43
44
45
46
47
48
49
50
52
5354
5557
5158
59
60
61
62
63
64
65
66
67
68
69
70
7172
73
74
75
5676
77
78
79
80
8182
83
84
85
86
87
88
89
90
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 4 The final deployment of nodes (BPSO)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
28
2938
3031
32
37366739
40
41
42
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44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
921527
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 5 The final deployment of nodes (GPSOmdashcrossover)
coverage problem Figures 4ndash7 are the final deployments ofnodes which are simulated from basic particle swarm opti-mization algorithm particle swarm optimization algorithmfused with crossover mutation idea from genetic algorithmparticle swarm optimization algorithm based on simulatedannealing and with compression factor and particle swarmoptimization algorithm based on simulated annealing andusing asynchronous learning factors Figure 8 is comparisonon best fitness value change in iteration process of eachalgorithm
After analyzing simulation results from each algorithmwe can see that simulation effect fromGPSO is the worst andSAPSOwith compression factor is the bestThe final purposeof particle movement is to improve network coverage bymoving redundant node and restoring network holes atthe meantime to avoid too much energy consumptionmoving distance of redundant node cannot be too far Ineach algorithm the nodes moving distance is controlled byparticle upper Vmax and lower Vmin bounds According to
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
45
46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
23
24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
43
44
45
46
47
48
50
51
52
5354 55
56
57
58
59
60
61
62
64
65
66
67
68
6971
72
7374
75
76
77
7899
79
80
8182
83
84
85
86
87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
International Journal of
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Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
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DistributedSensor Networks
International Journal of
Journal of Sensors 7
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
1527
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 3 The initial deployment of nodes
particle 119894 Monitor area is a square two-dimensional regionwherein origin of coordinate is square vertex at the lowerleft corner so both abscissa and ordinate of particle satisfy0 le 119909119894 119910119894le 119871 wherein 119871 is for side length of monitor area
Particle velocity V is for incremental of particle locationand can be expressed as V = V
1199091 V1199101 V1199092 V1199102 V
119909119894
V119910119894 V
119909119899 V119910119899 wherein each dimension element value of
velocity is corresponding to each dimension element valueof position and indicates corresponding coordinate valueschange To limit particle velocity upper Vmax and lower Vminbounds of particle velocity need to be set
Particle fitness value function is reciprocal value ofnetwork coverage based on gridswhich arementioned in Sec-tion 22 as shown in formula (22) So algorithm solving targetis network nodes coordinate distributionwhichminimize thefitness function value
min fitness = 1
120578=
119860119892
sum119860119892
119894=1119901119892(119866119894)
(22)
52 Experiment Result andAnalysis In this paper the solvingmethod for coverage restoring problem is simulated inMAT-LAB 2012a as experimental environment Nodes number119873 =
100 and monitor area side length 119871 = 500m nodes sensingradius 119877
119904= 30m nodes possibility sensing model parameter
119903 = 6m 120582 = 120573 = 05 and grids number 119860119892= 100 During
initialization nodes are deployed randomly and evenly inwhole monitor area and initial deployment of nodes is asshown in Figure 3 In this figure every dot is for nodesnumber beside is for node number and circle region is fornodes sensing region As shown in the figure there are 4obvious holes in initial deployment of nodes and the solvingtarget of network coverage problem is to move redundantnodes beside holes hence increasing network coverage
To verify effectiveness of particle swarm optimizationalgorithm which is based on simulated annealing this paperuses basic particle swarmoptimization algorithm and variousimproved algorithms to simulate and compare on network
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
5001
2
3
4
56
7
8
9 10
11
12
13
14
15
1617
18
193191
20
21
22
23
24
25
26
27
28
29
30
32
33
34
3536
3738
39
40
41
42
43
44
45
46
47
48
49
50
52
5354
5557
5158
59
60
61
62
63
64
65
66
67
68
69
70
7172
73
74
75
5676
77
78
79
80
8182
83
84
85
86
87
88
89
90
9293
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 4 The final deployment of nodes (BPSO)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
8456
7
8
10
11
12
1617
18
19
20
21
22
23
24
251355
26
28
2938
3031
32
37366739
40
41
42
43
44
45
46
47
48
49
50
51
52
5354
56
57
58
59
60
61
62
63
64
65
966
35
68
69
3470
71
72
7374
75
76
3377
78
79
80
14 8182
83
85
86
87
88
89
90
91
921527
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 5 The final deployment of nodes (GPSOmdashcrossover)
coverage problem Figures 4ndash7 are the final deployments ofnodes which are simulated from basic particle swarm opti-mization algorithm particle swarm optimization algorithmfused with crossover mutation idea from genetic algorithmparticle swarm optimization algorithm based on simulatedannealing and with compression factor and particle swarmoptimization algorithm based on simulated annealing andusing asynchronous learning factors Figure 8 is comparisonon best fitness value change in iteration process of eachalgorithm
After analyzing simulation results from each algorithmwe can see that simulation effect fromGPSO is the worst andSAPSOwith compression factor is the bestThe final purposeof particle movement is to improve network coverage bymoving redundant node and restoring network holes atthe meantime to avoid too much energy consumptionmoving distance of redundant node cannot be too far Ineach algorithm the nodes moving distance is controlled byparticle upper Vmax and lower Vmin bounds According to
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
45
46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
23
24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
43
44
45
46
47
48
50
51
52
5354 55
56
57
58
59
60
61
62
64
65
66
67
68
6971
72
7374
75
76
77
7899
79
80
8182
83
84
85
86
87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 Journal of Sensors
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500
12
3
4
5
6
7
8
9
10
11
12
13
14
15
1617
18
19
20
21
22
23
24
2526
27
28
29
30
31
32
33
35 36
37
38
39
40
41
42
43
44
45
46
47
8748
4950
51
52
53 54
55
3456
57
58
59
60
61
62 63
64
65
66
67 68
69
70
71
72
7374
75
76
77
78
79
80
8182
83
84
85
86
88
89
90
91
92
93
94
95
96
97
98
99
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 6 The final deployment of nodes (SAPSOmdashasynchronouslearning factors)
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
400
450
500 6312
3
4
6
7
8
910
11
12
13
14
3015
1617
18
19
20
21
22
23
24
25
26
27
28
2931
32
5 33
7034
3736
3835 39
40
41
4942
43
44
45
46
47
48
50
51
52
5354 55
56
57
58
59
60
61
62
64
65
66
67
68
6971
72
7374
75
76
77
7899
79
80
8182
83
84
85
86
87
88
89
90
91
92 93
94
95
96
97
98
100
x-axis 0sim500 (m)
y-a
xis 0sim500
(m)
Figure 7 The final deployment of nodes (SAPSOmdashcompressionfactor)
comparison experiment results when particle velocity upperand lower values are taken from Vmax = 002 sdot 119871 Vmin =
minusVmax this achieves the best experiment effect whereas ifexceeding network topology will change a lot and if less itwill be hard to restore hole Compared to other applicationsof PSO in network coverage problem the particle velocitymust be set as small so that the limitation will slow particlelocation change hence decreasing variety of particle swarmtherefore it will be hard to improve PSO performanceby using crossover mutation from genetic algorithm andexperiment shows that GPSO effect is even worse than BPSOeffect Both SAPSOwith compression factor and SAPSOwithasynchronous learning factors have good simulation effectAs shown in119892best variation curve algorithm can skip out localoptimum constantly to find better particle location As shownin final deployment of nodes the big holes among nodessensing circle almost disappear but there are still small holeshowever considering intruder mobility in monitor area the
0 100 200 300 600 700500400 800 900 10001
11
12
13
14
15
16
Particle swarm iteration number
BPSOGPSO (cross variation)SAPSO (band compression factor)SAPSO (asynchronous learning factor)
The o
ptim
al fi
tnes
s val
ue o
f par
ticle
swar
m o
ptim
izat
iong
best
Figure 8 The comparison chart of the best fitness value
intruder will inevitably enter nodes sensing region so smallholes can be ignored
6 Conclusion
As the wireless sensor actuator network usually work inpoor environment like battlefield fire and so forth it ismost likely to exhaust energy suffer irresistible damageor cause network coverage hole due to the long movingdistance This paper proposes a coverage restoring methodby moving nodes besides holes areas and transforming cov-erage restoring problem into nonconstrained optimizationproblem which takes network coverage ratio as optimizationtarget As it is hard to get analytical solution for this opti-mization problem swarm intelligence algorithm is neededto do random iterative search After comparison simulationresults from BPSO GPSO and SAPSO with nonconstrainedoptimization problem it verifies that simulated annealing canwell combine with particle swarm optimization algorithm tofulfill algorithm early global search and later local detectionSimulation proves that hybrid algorithm can effectively solvehole coverage problem in wireless sensor actuator network
Competing Interests
The authors declare that they have no competing interests
References
[1] L M Sun et al Wireless SensorNetwork Tsinghua UniversityPress 2005
[2] L LWang and X BWu ldquoDistributed detection and restorationon trap hole in sensor networksrdquo Control and Decision-Makingvol 27 no 12 pp 1810ndash1815 2012
[3] Z Lun Y Lu and C D Dong ldquoAn approach with ParticleSwarm Optimizer to optimize coverage in wireless sensor
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Journal of Sensors 9
networksrdquo Journal of Tongji University vol 37 no 2 pp 262ndash266 2009
[4] K Yang Q Liu S K Zhang et al ldquoAn algorithm to restoresensor network hole by moving nodesrdquo Journal on Communi-cations vol 33 no 9 pp 116ndash124 2012
[5] S Lee M Younis and M Lee ldquoConnectivity restorationin a partitioned wireless sensor network with assured faulttolerancerdquo Ad Hoc Networks vol 24 pp 1ndash19 2015
[6] I F Senturk K Akkaya and S Yilmaz ldquoRelay placement forrestoring connectivity in partitioned wireless sensor networksunder limited informationrdquo Ad Hoc Networks vol 13 pp 487ndash503 2014
[7] X Zhao and NWang ldquoOptimal restoration approach to handlemultiple actors failure in wireless sensor and actor networksrdquoIET Wireless Sensor Systems vol 4 no 3 pp 138ndash145 2014
[8] Y Zou and K Chakrabarty ldquoSensor deployment and targetlocalization based on virtual forcesrdquo in Proceedings of the22nd Annual Joint Conference on the IEEE Computer andCommunications Societies pp 1293ndash1303 San Francisco CalifUSA April 2003
[9] Y Bejerano ldquoSimple and efficient k-coverage verification with-out location informationrdquo in Proceedings of the 27th IEEE Com-munications Society Conference on Computer Communications(INFOCOM rsquo08) pp 897ndash905 IEEE Phoenix Ariz USA April2008
[10] J Kennedy ldquoParticle swarm optimizationrdquo in Encyclopedia ofMachine Learning pp 760ndash766 Springer New York NY USA2010
[11] W Z Guo andG L ChenDiscrete Particle SwarmOptimizationAlgorithm and Application Tsinghua University Press BeijingChina 2012
[12] M Clerc and J Kennedy ldquoThe particle swarm-explosion sta-bility and convergence in a multidimensional complex spacerdquoIEEE Transactions on Evolutionary Computation vol 6 no 1pp 58ndash73 2002
[13] J C Bansal P K Singh M Saraswat A Verma S S Jadonand A Abraham ldquoInertia weight strategies in particle swarmoptimizationrdquo in Proceedings of the 3rd World Congress onNature and Biologically Inspired Computing (NaBIC rsquo11) pp633ndash640 IEEE Salamanca Spain October 2011
[14] J Xin G Chen and Y Hai ldquoA particle swarm optimizer withmulti-stage linearly-decreasing inertia weightrdquo in Proceedingsof the International Joint Conference on Computational Sciencesand Optimization (CSO rsquo09) vol 1 pp 505ndash508 Sanya ChinaApril 2009
[15] A Nikabadi and M Ebadzadeh ldquoParticle swarm optimizationalgorithms with adaptive inertia weight a survey of the stateof the art and a Novel methodrdquo IEEE Journal of EvolutionaryComputation In press
[16] R C Eberhart and Y Shi ldquoTracking and optimizing dynamicsystems with particle swarmsrdquo in Proceedings of the Congresson Evolutionary Computation vol 1 pp 94ndash100 IEEE SeoulSouth Korea May 2001
[17] A Ratnaweera S K Halgamuge and H C Watson ldquoSelf-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficientsrdquo IEEE Transactions on Evolu-tionary Computation vol 8 no 3 pp 240ndash255 2004
[18] K Premalatha and A M Natarajan ldquoHybrid PSO and GA forglobalmaximizationrdquo International Journal of Open Problems inComputer Science and Mathematics vol 2 no 4 pp 597ndash6082009
[19] B Liu LWang Y-H Jin F Tang and D-X Huang ldquoImprovedparticle swarm optimization combined with chaosrdquo ChaosSolitons amp Fractals vol 25 no 5 pp 1261ndash1271 2005
[20] T A A Victoire and A E Jeyakumar ldquoHybrid PSOndashSQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004
[21] H Lu P Sriyanyong Y H Song and T Dillon ldquoExperimentalstudy of a new hybrid PSO with mutation for economicdispatch with non-smooth cost functionrdquo International Journalof Electrical Power amp Energy Systems vol 32 no 9 pp 921ndash9352010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of