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基于Tent映射和Logistic映射的粒子群优化算法(英文).docx

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基于Tent映射和Logistic映射的粒子群优化算法(英文) Particleswarmoptimization(PSO)isapopularmeta-heuristicalgorithmforsolvingvariousoptimizationproblems.Itisapopulation-basedapproachthatutilizestheconceptofaswarmofparticlestonavigatethesearchspacetowardstheoptimalsolution.Inrecentyears,severalmodificationstothebasicPSOalgorithmhavebeenproposedtoimproveitsperformance,includingtheuseofchaoticmapsforparticlebehavior.Inthispaper,weproposeaPSOalgorithmbasedontwochaoticmaps,TentandLogisticmaps,toenhancetheexplorationandexploitationcapabilitiesofthealgorithm. TheTentmapisapiecewiselinearmapthatgenerateschaoticdynamicsfromaboundedinterval.Itisgivenbytheiterativeformula: x[n+1]=2rx[n]if0≤x[n]<0.5 x[n+1]=2r(1−x[n])if0.5≤x[n]<1 wherex[n]isthestateofthesystemattimen,risthemapparameter,andtheinitialstatex[0]isavaluebetween0and1.TheTentmaphasamaximumLyapunovexponentofln(2)andexhibitssensitivitytoinitialconditions,makingitsuitableforgeneratingrandomsequencesforoptimizationproblems. TheLogisticmapisanotherpopularchaoticmapthatgeneratesdifferenttypesofdynamics,dependingonthevaluesofitsparameterr.Itisgivenbytheiterativeformula: x[n+1]=rx[n](1−x[n]) wherex[n]isthestateofthesystemattimenandristhemapparameter.TheLogisticmapexhibitsperiodic,chaotic,andhyperchaoticbehaviorsfordifferentvaluesofr.Itiscommonlyusedinchaoticoptimizationalgorithmsduetoitssimpleformandversatility. TheproposedPSOalgorithmbasedontheTentandLogisticmaps(TLPSO)usestheTentmaptoinitializetheparticles'positionandvelocityandtheLogisticmaptoupdatetheirpositionandvelocity.Thealgorithmstartsbyrandomlyinitializingaswarmofparticlesinthesearchspace.Eachparticleisrepresentedbyapositionvectorxandavelocityvectorv,bothofwhichareupdatedbasedonthebestglobalandlocalsolutionsfoundinthesearchspace. ThepositionandvelocityupdateequationsinTLPSOaregivenby: v[i,j](t+1)=wv[i,j](t)+c1r1(x_best[j]−x[i,j](t))+c2r2(p_best[i,j]−x[i,j](t)) x[i,j](t+1)=φ(x[i,j](t)+v[i,j](t+1)) wherev[i,j]andx[i,j]denotethevelocityandpositionofthei-thparticleinthej-thdimension,respect