差分演化的收敛性分析与算法改进

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1、万方数据ISSN1000—9825，CODENRUXUEWJournalofSoftware，V01．21，No．5，May2010，PP．875—885doi：10．3724／SEJ．1001．2010．034860byInstituteofSoftware．肪PChineseAcademyofSciences．Allrightsrcscawed．差分演化的收敛性分析与算法改进·贺毅朝1+，王熙照2，刘坤起13，王彦祺11(石家庄经济学院信息工程学院，河北石家庄050031)2(河北大学数学与计算机学院，

2、河北保定071002)3(中国地质大学计算机学院，湖北武汉430074)ConvergentAnalysisandAlgorithmicImprovementofDifferentialEvolutionHEYi·Cha01+，WANGXi．Zha02，LIUKtm．Qilj，WANGYan．Qil1(SchoolofInformationEngineering，ShijiazhuangUniversityofEconomics，Shijiazhnang050031，China)2(CollegeofMat

3、hematicsandComputerScience，HebeiUniversity，Baoding071002，China)3(SchoolofComputer,ChinaUniversityofGeosciences，Wuhan430074，China)+Correspondingauthor：E-marl：heyichao@sjzue．eAu．cnE·mail：jos@iscas．∞．cnhttp：／1www．jos．org．cnTcl停缸：+86．10-62562563HeYC，Wangxz,Llu

4、KQ，WangYQ．ConvergentanalysisandalgorithmicImprovementofdifferentialevolution·JournalofSoftware,2010。21(5)：875—885．http：／／www．jos．org．cn／1000·9825／3486．htmAbstract：Toanalyzetheconvergenceofdifferentialevolution(DE)andenhanceitscapabilityandstability，thispap

5、erfirstdefinesadifferentialoperator(DO)asarandommappingfromthesolutionspacetotheCartesianproductofsolutionspace，andprovestheasymptoticconvergenceofDEbasedontherandomcontractionmappingtheoreminrandomfunctionalanalysistheory．Then，inspiredby“quasi—physicalper

6、sonificationalgorithm”。thispaperproposesanimproveddifferentialevolutionwithmulti·strategycooperatingevolution(MEDE)isaddressedbasedonthefactthateachevolutionstrategyofDEhascommonpeculiaritybutdifferentcharacteristics．Itsasymptoticconvergenceisgivenwiththed

7、efinitionofmulti—strategydifferentialoperator(MDO)，andtheconnotativepeculiarityofMEDEisanalyzed．ComparedwiththeoriginalDE，DEfirDEandDEfirSPX，thesimulationresultson5classicalbenchmarkfunctionsshowthatMEDEhasobviousadvantagesintheconvergencerate，solution—qua

8、lityandadaptability．Itissuitableforsolvingcomplexhigh·dimensionnumeraloptimizationproblems．Keywords：differentialevolution；asymptoticconvergence；contractionmapping；randomoperator；evolutionstrategy摘要：为了分析差分演化(d