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1、AGeneticAlgorithmforSolvingaClassofMulti-objectiveBilevelProgrammingProblemsShanfengZhang,KeqiangLiDepartmentofComputer,******University,Guangzhou,810008,ChinaAbstractAtpresent,mostoftheresearchesonbilevelprogrammingproblemsarefocusedonsingleobjectivecases.Thispaperdiscussesabilevelprog
2、rammingproblemwithupperlevelmulti-objectiveoptimization.Inordertosolvetheproblemefficiently,wepresentageneticalgorithmusinginterpolation.Thismethoddoesnotrequiresolvingloweroptimizationproblemfrequently.Intheproposedalgorithm,firstly,theinterpolationfunctionsareadoptedtoapproximatelower
3、levelsolutionfunctions.Asaresult,theoriginalproblemcanbeapproximatedbyasingle-levelmulti-objectiveprogramming.Inaddition,thecorrespondinginterpolationfunctionsareupdatedsuchthatthesefunctionscanapproximatethelowerlevelsolutionfunctionverywell.Finally,themulti-objectiveprogrammingissolve
4、dforobtaininganoptimalsolutionsetoftheoriginalproblem.Thesimulationontwoexamplesindicatestheproposedalgorithmiseffectiveandfeasible.Keywords:multi-objectivebilevelprogramming,geneticalgorithm,interpolation.1.IntroductionBilevelprogrammingproblem(BLPP)isahierarchicaloptimizationproblem,w
5、hichincludesanupperlevelsdecisionmakerandalowerlevelsdecisionmaker.Bothofthemhavetheobjectivefunctionsandconstraintconditions.ThisproblemwasproposedbyStackelberg[1],andknownasStackelbergproblem.Themathematicalmodelofthiskindofproblemscanbewrittenasfollows:(1)Wherearedecisionvariables,ar
6、eobjectivefunctionsandareconstraintfunctions;aretheothersconstraint,suchasupperandlowerboundsorintegerconstraints.Bilevelprogrammingproblemsoccurinvariousapplications,suchaseconomicsandmanagement[2],engineering[3],transportationandothers.Mostofthesemodelsarebilevelsingleobjectiveproblem
7、s.Infact,therearelotsofreal-worldproblemsthatcanbemodeledasmulti-objectivebilevelprogrammingproblems[4].Inamulti-objectivebilevelproblematleastonedecisionmakerhasmorethanoneobjectivefunction,andtheseobjectivesconflictwitheachother.Inrecentyears,multi-objectivebilevelprogramming
