粒子群优化算法种群规模的选择

2010195ResearchandDevelopment125雰1121(1.423000;2.510310)22060100200204060804PopulationSizeSelectionofParticleSwarmOptimizerAlgorithmZHANGWen-Fen1,WANGGang1,ZHUZhao-Hui2,XIAOJuan1(1.FacultyofComputer,XiangnanUniversity,Chenzhou423000,China;2.GuangzhouGCIPlan&DesignInstituteofCommunicationEngineering,Guangzhou510310,China)Abstract:Thispapergivesadviceonpopulationsizeselectionfromliteraturesandanalyzestherelationsbetweenpopulationsize,dimension,precisionandstability.Itproposesamethodofpopulationsizeselection.Twobenchmarkfunctionsareemployedtoperformfunctionoptimizationwithdifferentdimensions:20,60,100and200.Foreachdimension,populationsizeissetto20,40,60and80.Thispaperanalyzestheresultsandproposesageneralpopulationsize.Furthermore,anapproachbasedonexperimentsisproposedforpopulationsizeselection.Withtheapproach,arelationgraphofpopulationsize,timeandprecisioncanbeusedtodeterminetheoptimumpopulationsize.Keywords:PSO;populationsize;dimension;functionoptimization(ParticleSwarmOptimizer,PSO)[1]1995KenndyEberhartPSOPSO2PSizePSO:(09C921):2009-09-28;:2009-11-08ShiEberhartPSO[2][3]30[4]2050[5]3040PSize1PSO2010195126ResearchandDevelopmentPSOPSODnkiDkiRX∈kiP),,2,1(niPki⋅⋅⋅=kgPDkiRV∈k+1(1)(2)[1](1)(2)c1c2r1r2[0,1]ShiEberhart[6][-Vmax,Vmax](1)(2)22.1PSOT[7]PSOMATLAB7.0PSOc1c220.90.442(3)(4)f1-418.98333nf20f1∈ix[-500,500]f2∈ix[-600,600]2n42060100200PSize420406080PSize16PSO1002.2f1f2122060100200100txtx12f12080201.332001.9520200f220204020040201012PSizef120406040601002004080f220040PSizef1603F160100PSize34011122()()kkkkkkiiiigiVVcrPXcrPXω+=+−+−1kkkiiiXXV+=+11()(sin())niiifxxx==−∑21111002()(100)cos()14000nniiiixfxxi==−=−−+∑∏2010195ResearchandDevelopment127508010080T1)xT2)y3)f160310000160x30000y608060803YyYx4240405080PSO1f12f22010195128ResearchandDevelopment3f1601001KenndyJ,EbethartRC.ParticleSwarmOptimization.Proc.ofthe1995IEEEInternationalConferenceonNeuralNetworks,Piscataway,NJ,USA,1995,19421948.2ShiY,EberhartRC.EmpiricalStudyofParticleSwarmOptimization.1999CongressonEvolutionaryCom-puting,1999,Vol.III:19451950.3CarlisleA,DozierG.AnOff-The-ShelfPSO.Proc.oftheWorkshoponParticleSwarmOptimization.2001.16.(136)2OutputVoltage3.9084.2OutputRipple20mVp-pOutputCurrent0.12AInductorPeaktoPeakCurrent0.150.6A664,,..,2008,27(1):7680.5,.PSO.,2007,(6):13.6ShiY,EberhartRC.AmodifiedParticleSwarmOptimizer.IEEEInternationalConferenceonEvolu-tionaryComputationProceedings,Anchorage,AK,USA,1998.6973.7BirgeB.Psot-aparticleswarmoptimizationforusewithmatlab.InSIS03Proceedingsofthe2003IEEE,SwarmIntelligenceSymposium,April2003.182186.GPRS230mA86%1,,..,2004,25(9):5457.2..,2005,20(3):6770.3,,..,2007,10:6769.4,,..:,2007.5LabrosseJJ..uC/OS-II(2).:,2003.