Research Article Hybrid Wireless Sensor Network...

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


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


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


sdot 119905

1198882= 119888min +


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


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


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y-a

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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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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


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


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


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



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


O4 O1

O3

O2



120591 =12 sdot sum

119894120577 (119894)

119899 (119899 minus 1) 2=

sum119894120577 (119894)

119899 (119899 minus 1) (4)




119904and communi-


119888ge 2 sdot119877










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)


grids 119866119894and nodes 119873








119901119892(119866119894) = 1 minus

119860119899

prod

119895=1

(1 minus 119901119892119899

(119866119894 119873119895)) (6)



120578 =

sum119860119892

119894=1119901119892(119866119894)

119860119892

(7)








119894= (119909(119905)

1198941 119909(119905)

1198942 119909

(119905)

119894119898) 119894 = 1 2 119899 and speed


119894= (V(119905)1198941 V(119905)1198942 V(119905)

119894119898) 119894 =


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)




1


119894119889is for 119889th-


119889










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


10038161003816100381610038161003816

119862 = 1198881+ 1198882

(11)



follows


0729


2= 13 119862





119905max (12)





119908

=



119908max 119891 gt 119891avg

(13)


119908 = 120583 + 120590 sdot 119873 (0 1)




1= 1198882= 2 there are




is as follows

1198881= 1198882= 119888max minus


sdot 119905 (15)








1198881= 119888max minus


sdot 119905

1198882= 119888min +


sdot 119905

(16)





Vchild =


10038161003816100381610038161003816

sdot10038161003816100381610038161003816Vparent

10038161003816100381610038161003816 (18)















119894 Take



value


1198790=

119891 (119901119892)

ln 5 (19)


119891(119901119892) of each particle119901



TF (119901119894) =

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

sumpop119894=1

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

(20)







119879119896+1

= 120582 sdot 119879119896 (21)




1199091 1199101 1199092 1199102 119909

119894 119910119894 119909




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)




1199091 V1199101 V1199092 V1199102 V

119909119894

V119910119894 V




min fitness = 1

120578=

119860119892

sum119860119892

119894=1119901119892(119866119894)

(22)







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)


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)





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)


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)




0 100 200 300 600 700500400 800 900 10001

11

12

13

14

15

16



The o

ptim

al fi

tnes

s val

ue o

f par

ticle

swar

m o

ptim

izat

iong

best



6 Conclusion


Competing Interests


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










O4 O1

O3

O2



120591 =12 sdot sum

119894120577 (119894)

119899 (119899 minus 1) 2=

sum119894120577 (119894)

119899 (119899 minus 1) (4)




119904and communi-


119888ge 2 sdot119877










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)


grids 119866119894and nodes 119873








119901119892(119866119894) = 1 minus

119860119899

prod

119895=1

(1 minus 119901119892119899

(119866119894 119873119895)) (6)



120578 =

sum119860119892

119894=1119901119892(119866119894)

119860119892

(7)








119894= (119909(119905)

1198941 119909(119905)

1198942 119909

(119905)

119894119898) 119894 = 1 2 119899 and speed


119894= (V(119905)1198941 V(119905)1198942 V(119905)

119894119898) 119894 =


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)




1


119894119889is for 119889th-


119889










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


10038161003816100381610038161003816

119862 = 1198881+ 1198882

(11)



follows


0729


2= 13 119862





119905max (12)





119908

=



119908max 119891 gt 119891avg

(13)


119908 = 120583 + 120590 sdot 119873 (0 1)




1= 1198882= 2 there are




is as follows

1198881= 1198882= 119888max minus


sdot 119905 (15)








1198881= 119888max minus


sdot 119905

1198882= 119888min +


sdot 119905

(16)





Vchild =


10038161003816100381610038161003816

sdot10038161003816100381610038161003816Vparent

10038161003816100381610038161003816 (18)















119894 Take



value


1198790=

119891 (119901119892)

ln 5 (19)


119891(119901119892) of each particle119901



TF (119901119894) =

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

sumpop119894=1

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

(20)







119879119896+1

= 120582 sdot 119879119896 (21)




1199091 1199101 1199092 1199102 119909

119894 119910119894 119909




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)




1199091 V1199101 V1199092 V1199102 V

119909119894

V119910119894 V




min fitness = 1

120578=

119860119892

sum119860119892

119894=1119901119892(119866119894)

(22)







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)


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)





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)


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)




0 100 200 300 600 700500400 800 900 10001

11

12

13

14

15

16



The o

ptim

al fi

tnes

s val

ue o

f par

ticle

swar

m o

ptim

izat

iong

best



6 Conclusion


Competing Interests


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119894= (119909(119905)

1198941 119909(119905)

1198942 119909

(119905)

119894119898) 119894 = 1 2 119899 and speed


119894= (V(119905)1198941 V(119905)1198942 V(119905)

119894119898) 119894 =


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)




1


119894119889is for 119889th-


119889










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


10038161003816100381610038161003816

119862 = 1198881+ 1198882

(11)



follows


0729


2= 13 119862





119905max (12)





119908

=



119908max 119891 gt 119891avg

(13)


119908 = 120583 + 120590 sdot 119873 (0 1)




1= 1198882= 2 there are




is as follows

1198881= 1198882= 119888max minus


sdot 119905 (15)








1198881= 119888max minus


sdot 119905

1198882= 119888min +


sdot 119905

(16)





Vchild =


10038161003816100381610038161003816

sdot10038161003816100381610038161003816Vparent

10038161003816100381610038161003816 (18)















119894 Take



value


1198790=

119891 (119901119892)

ln 5 (19)


119891(119901119892) of each particle119901



TF (119901119894) =

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

sumpop119894=1

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

(20)







119879119896+1

= 120582 sdot 119879119896 (21)




1199091 1199101 1199092 1199102 119909

119894 119910119894 119909




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)




1199091 V1199101 V1199092 V1199102 V

119909119894

V119910119894 V




min fitness = 1

120578=

119860119892

sum119860119892

119894=1119901119892(119866119894)

(22)







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)


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)





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)


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)




0 100 200 300 600 700500400 800 900 10001

11

12

13

14

15

16



The o

ptim

al fi

tnes

s val

ue o

f par

ticle

swar

m o

ptim

izat

iong

best



6 Conclusion


Competing Interests


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119908

=



119908max 119891 gt 119891avg

(13)


119908 = 120583 + 120590 sdot 119873 (0 1)




1= 1198882= 2 there are




is as follows

1198881= 1198882= 119888max minus


sdot 119905 (15)








1198881= 119888max minus


sdot 119905

1198882= 119888min +


sdot 119905

(16)





Vchild =


10038161003816100381610038161003816

sdot10038161003816100381610038161003816Vparent

10038161003816100381610038161003816 (18)















119894 Take



value


1198790=

119891 (119901119892)

ln 5 (19)


119891(119901119892) of each particle119901



TF (119901119894) =

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

sumpop119894=1

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

(20)







119879119896+1

= 120582 sdot 119879119896 (21)




1199091 1199101 1199092 1199102 119909

119894 119910119894 119909




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)




1199091 V1199101 V1199092 V1199102 V

119909119894

V119910119894 V




min fitness = 1

120578=

119860119892

sum119860119892

119894=1119901119892(119866119894)

(22)







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)


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)





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)


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)




0 100 200 300 600 700500400 800 900 10001

11

12

13

14

15

16



The o

ptim

al fi

tnes

s val

ue o

f par

ticle

swar

m o

ptim

izat

iong

best



6 Conclusion


Competing Interests


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















119894 Take



value


1198790=

119891 (119901119892)

ln 5 (19)


119891(119901119892) of each particle119901



TF (119901119894) =

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

sumpop119894=1

exp (minus (119891 (119901119894) minus 119891 (119901

119892)) 119905)

(20)







119879119896+1

= 120582 sdot 119879119896 (21)




1199091 1199101 1199092 1199102 119909

119894 119910119894 119909




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)




1199091 V1199101 V1199092 V1199102 V

119909119894

V119910119894 V




min fitness = 1

120578=

119860119892

sum119860119892

119894=1119901119892(119866119894)

(22)







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)


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)





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)


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)




0 100 200 300 600 700500400 800 900 10001

11

12

13

14

15

16



The o

ptim

al fi

tnes

s val

ue o

f par

ticle

swar

m o

ptim

izat

iong

best



6 Conclusion


Competing Interests


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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)




1199091 V1199101 V1199092 V1199102 V

119909119894

V119910119894 V




min fitness = 1

120578=

119860119892

sum119860119892

119894=1119901119892(119866119894)

(22)







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)


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)





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)


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)




0 100 200 300 600 700500400 800 900 10001

11

12

13

14

15

16



The o

ptim

al fi

tnes

s val

ue o

f par

ticle

swar

m o

ptim

izat

iong

best



6 Conclusion


Competing Interests


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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)


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)




0 100 200 300 600 700500400 800 900 10001

11

12

13

14

15

16



The o

ptim

al fi

tnes

s val

ue o

f par

ticle

swar

m o

ptim

izat

iong

best



6 Conclusion


Competing Interests


References


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Hybrid Wireless Sensor Network...

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Transcript of Research Article Hybrid Wireless Sensor Network...