一种结合自适应惯性权重的混合粒子群算法

21320166JOUＲNALOFHAＲBINUNIVEＲSITYOFSCIENCEANDTECHNOLOGYVol.21No.3Jun．201612341.6100442.6114333.1500014.150001particleswarmoptimizationPSO..、、.DOI10．15938/j．jhust．2016．03．010TP391.4A1007－2683201603－0049－05AHybridParticleSwarmOptimizationAlgorithmwithAdaptiveInertiaWeightYUGui-qin12LILiu-dong3YUANYong-feng41.SchoolofComputerScienceandTechnologySichuanUniversityChengdu610044China2.PublicEducationDepartmentChengduArtVocationalCollegeChengdu611433China3.CollegeofScienceHarbinInstituteofTechnologyHarbin150001China4.SchoolofComputerScienceandTechnologyHarbinInstituteofTechnologyHarbin150001ChinaAbstractParticleswarmoptimizationalgorithmisanoptimizationalgorithmwhichisefficientandeasytoim-plementbutthealgorithmismoresensitivewithvariousparameters.Inthispaperweresearchtheclassicalparti-cleswarmoptimizationalgorithmintheviewofitsshortcomingsthatiseasytofallintolocaloptimumandthenputsforwardtheideaofusingadaptiveinertiaweightsandintroducingthesimulatedannealingmethodtoclassicalparti-cleswarmoptimizationalgorithmstosolvetheproblemthatlocaloptimalsolutionofclassicalparticleswarmoptimi-zationalgorithm.Comparedwiththeclassicalalgorithmthesimulationresultsshowthattheproposedhybridalgo-rithmcannotonlyavoidthelocaloptimalsolutionintheprocessofparticleswarmoptimizationbutalsohasthecharacteristicsoffastconvergencehighsuccesstimesstabilityandgoodresults.Keywordsself-adaptationinertiaweightsimulatedannealingparticleswarmoptimizationhybridalgorithm2016－01－226117214961402132.1978—1992—.1979—[e-mail].0、、1.1997KennedyEberhart2、1998Y.Shi3、20084.“”5－6.7－9Metropolis.22.110－11.1、.vidt+1=ωvidt+c1r1pidt－xidt+c2r2pgd－xidtxidt+1=xidt+vidt+1}1vid＞Vmaxvid=Vmaxvid＜Vminvid=Vmini=12…md=12…Dωc1c2r1r201xidipidipgdvidivid∈VminVmax.PbestGbest.PbestGbest.Gbest12－13...12.2、、、.simulatedannea-lingSAMetropolis1953Kirkpatrick、Gelett1982.SA、.14.Metropolis、1、p.、、.15.3...Metropolisp0521.3.1.2ωt=ωstart－ωendtan0.8751－ttmaxk+ωend2ωstart0.9ωend0.48ttmaxkω.1kk0.10.02940.02760.20.03000.02230.30.03290.02480.40.02660.01910.50.02580.02780.60.02540.02070.70.03150.03070.80.03000.03430.90.03010.02351.00.02640.02671.10.03020.02301.20.03550.01941.30.04130.02911.40.02300.02121.50.02890.02731.60.02630.02001.70.02610.01981.80.03340.02191.90.02570.02532.00.02800.0256kGriewank20.1k0.40.61.41.7Grie-wankk=0.6k=1.7k.k=0.62002k=0.63k=1.7k=1.7800.k=0.6k=1.7k=0.623ωt=ωstart－ωendtan0.8751－ttmax0.6+ωend3vidt+1=ωtvidt+c1r1pidt－xidt+c2r2pgd－xidtxidt+1=xidt+vidt+1}43.2Metropolisxifxi.pbestfpbestΔf=fxi－f153pbestp=expΔf/TT.fxi＞fpbestxifxi＜fpbest.Metropolisfxi＞fpbestxip=expΔf/Trand01p=expΔf/T＞rand01xi.gbestGbestMetropolis15－174.T、xi、v、tmax、pi、pg、fxGbestfort=1tmaxfori=1miffxi＞fpiorexpfxi－fpi/T＞rand01pi=xiiffpi＞fpgorexpfpi－fpg/T＞rand01pg=xbestvi=vvixiwith4tov'ix'iandωwith3iffx'i＞fxiorexpfx'i－fxi/T＞rand01Gbest=x'iTt44Sphere、Grie-wank18－20particlewwarmoptimizationbaseonmutativeparametersP-PSOparticleswarmoptimizationbaseonmutativepa-rametersandsimulatedannealingP-PSO-SA.1SphereSphere5.fx=∑ni=1x2i－100!xi!1005xi=00.ω=0.7P-PSOP-PSO-SAωstart=0.9ωend=0.4.c1=c2=2tmax=150T=2000k=0.9510－6.350Matlab52.5Sphere2Sphere/sPSO1050.26454420.1343920.7238P-PSO1030.21347450.1313920.5591P-PSO-SA960.19933480.091335.200054Sphere.2P-PSO-SA、、、、..2GriewankGriewank、、Griewank6.fx=14000∑ni=1x2i－∏ni=1xi槡i+162521SphereMatlab63.6Griewank3Griewank/sPSO1000.1136210.267021.288P-PSO950.1105350.193521.218P-PSO-SA920.0898400.02565.2876Griewank...3、、、、.5...、、、、.1INDIＲAKKANMANIS.AssociationＲuleMiningThroughA-daptiveParameterControlinParticleSwarmOptimizationＲ.BerlinHeidelbergSpringer-Verlag2014.2JAMESKennedyＲUSSELLCEBEＲHAＲT.ADircreteBinaryVersionoftheParticleSwarmAlgorithmC∥IEEEInternationalConferenceonSystems19974104－4108.3SHIYuhuiＲUSSELLEberhart.AModifiedParticleSwarmOpti-mizerC∥IEEEWorldCongressonComputationalIntelligence199869－73.4.J.20083661242－1248.5.M.200935－64.6.M.200813－14.7LIUDongsheng.ImprovedGeneticAlgorithmBasedonSimulatedAnnealingandQuantumComputingStrategyforMiningAssociationＲulesJ.JournalofSoftware20101151243－1249.8.PSO-SAD.2013.9.J.201347101723－1730.10.M.20106－7.11.PSOPFSPJ.201217615－16.12.M.201051－72.13.J.201015651－52.14.J.2014124153－156.15ALAZAMIＲSＲEBENNACKSPAＲDALOSPM.Chapter18Im-provingtheNeighborhoodSelectionStrategyinSimulatedAnnealingUsingOptimalStoppingProblem.InGlobalOptimizationFocusonSimulatedAnnealingJ.EnergySystems2008363－382.16NISHIMOＲIH.ComparisonofQuantumAnnealingandSimulatedAnnealingC∥TheEuropeanPhysicalJournalSpecialTopics201515－16.17FEＲＲANTENeriEＲNESTOMininnoGIOVANNIIacca.Com-pactParticleSwarmOptimizationJ.InformationScience201323996－121.18YANGChaoKUMAＲMrinal.AnInformationGuidedFrameworkforSimulatedAnnealingC∥JournalofGlobalOptimization201562131－154.19LUOYongZHUBoTANGYong.SimulatedAnnealingAlgo-rithmforOptimalCapitalGrowthC∥PhysicaA-statisticalMe-chanicsandItsApplications201440810－18.20.J.2014476874－880.353