ParticleSwarmOptimizationYuhuiShiElectronicDataSystems,Inc.YuhuiShiKokomo,IN46902,USAAbstract.ThispapersurveystheresearchanddevelopmentofPSOinfivecategories:algorithms,topology,parameters,hybridPSOalgorithms,andapplications.1.IntroductionEuclideanneighborhoodwasutilizeddesigneddynamicallychangingVmax(KennedyandEberhart1995,EberhartmightimprovethePSO'sperformanceFeatureArticleParticleswarmoptimization(PSO)isandKennedy1995,Eberhart,Simpson(FanandShi2001).ElectronicDataSystems,oneInc.oftheevolutionarycomputationandDobbins1996).TheoriginalPSOThePSOalgorithmissimpleincon-techniques.Liketheotherevolutionaryalgorithmisdescribedasbelow:cept,easytoimplementandcomputa-computationtechniques,PSOisapopu-tionalefficient.Theoriginalprocedureforlation-basedsearchalgorithmandisini-vid=vid+c1rand()(pid-xid)+c2Rand()(pgd-xid)(1a)implementingPSOisasfollows:tializedwithapopulationofrandomsolu-xid=xid+vid(1b)tions,calledparticles.Unlikeintheother1.Initializeapopulationofparticleswithevolutionarycomputationtechniques,wherec1andc2arepositiveconstants,randompositionsandvelocitiesonDeachparticleinPSOisalsoassociatedandrand()andRand()aretworandomdimensionsintheproblemspace.withavelocity.Particlesflythroughthefunctionsintherange[0,1];Xi=(xi1,xi2,2.Foreachparticle,evaluatethedesiredsearchspacewithvelocitieswhichare…,xiD)representstheithparticle;Pi=optimizationfitnessfunctioninDvari-dynamicallyadjustedaccordingtotheir(p,p,…,p)representsthebestpre-ables.historicalbehaviors.Therefore,theparti-i1i2iD3.Compareparticle'sfitnessevaluationviousposition(thepositiongivingthecleshaveatendencytoflytowardsthewithitspbest.Ifcurrentvalueisbetterbestfitnessvalue)oftheithparticle;thebetterandbettersearchareaoverthethanpbest,thensetpbestequaltothesymbolgrepresentstheindexofthecourseofsearchprocess.Sinceitsintro-currentvalue,andPequalstothecur-bestparticleamongalltheparticlesiniductionin1995(KennedyandEberhartthepopulation;V=(v,v,…,v)rep-rentlocationXiinD-dimensional1995,Eberha