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1、1000-9825/2003/14(07)1243©2003JournalofSoftware软件学报Vol.14,No.7∗Pareto强度值演化算法求解约束优化问题1,2+222周育人,李元香,王勇,康立山1(华南理工大学计算机科学与工程学院,广东广州510640)2(武汉大学软件工程国家重点实验室,湖北武汉430072)AParetoStrengthEvolutionaryAlgorithmforConstrainedOptimization1,2+222ZHOUYu-Ren,LIYuan-Xiang,WANGYong,KANGLi-Shan1(Colle
2、geofComputerScienceandEngineering,SouthChinaUniversityofTechnology,Guangzhou510640,China)2(StateKeyLaboratoryofSoftwareEngineering,WuhanUniversity,Wuhan430072,China)+Correspondingauthor:E-mail:zhouyuren@hotmail.comReceived2002-08-12;Accepted2002-10-17ZhouYR,LiYX,WangY,KangLS.AParetos
3、trengthevolutionaryalgorithmforconstrainedoptimization.JournalofSoftware,2003,14(7):1243~1249.http://www.jos.org.cn/1000-9825/14/1243.htmAbstract:Anewapproachispresentedtohandleconstraintsoptimizationusingevolutionaryalgorithms.Itneitherusesanypenaltyfunctionnormakesdistinctionbetwee
4、nfeasiblesolutionsandinfeasiblesolutions.Thenewtechniquetreatsconstrainedoptimizationasatwo-objectiveoptimization.Oneobjectiveisoriginalobjectivefunction,theotheristhedegreeviolatingtheconstraints.Individual’srankingprocedureisbasedonitsParetostrengthwhichappearsfirstinmulti-objectiv
5、eoptimization.Paretostrengthevaluatesanindividual’sfitnessdependentonthenumberofdominatedpointsinthepopulation.BycombiningParetostrengthrankingprocedurewithminimalgenerationgapmodal,anewreal-codedgeneticalgorithmisproposed.Thenewapproachiscomparedagainstotherevolutionaryoptimizationt
6、echniquesinseveralbenchmarkfunctions.Theresultsobtainedshowthatthenewapproachisageneral,effectiveandrobustmethod.Itsperformanceoutperformssomeothertechniques.Especiallyforsomecomplicatedoptimizationproblemswithinequalityandequalityconstraints,theproposedmethodprovidesbetternumericala
7、ccuracy.Keywords:evolutionaryalgorithm;constrainedoptimization;multi-objective;Paretostrength摘要:提出了一种求解约束函数优化问题的方法.它不使用传统的惩罚函数,也不区分可行解和不可行解.新的演化算法将约束优化问题转换成两个目标优化问题,其中一个为原问题的目标函数,另一个为违反约束条件的程度函数.利用多目标优化问题中的Pareto优于关系,定义个体Pareto强度值指标以便对个体进行排序选优,根据Pareto强度值排序和最小代数代沟模型设计出新的实数编码遗传算法.对常见测
8、试函数的数值实验证实了新
