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1、AGeneticAlgorithmforSolvingaClassofMulti-objectiveBilevelProgrammingProblemsShanfengZhang,KeqiangLiDepartmentofComputer,******University,Guangzhou,810008,ChinaAbstractAtpresent,mostoftheresearchesonbilevelprogrammingproblemsarefocusedonsingleobjectivecases.Thispa
2、perdiscussesabilevelprogrammingproblemwithupperlevelmulti-objectiveoptimization.Inordertosolvetheproblemefficiently,wepresentageneticalgorithmusinginterpolation.Thismethoddoesnotrequiresolvingloweroptimizationproblemfrequently.Intheproposedalgorithm,firstly,thein
3、terpolationfunctionsareadoptedtoapproximatelowerlevelsolutionfunctions.Asaresult,theoriginalproblemcanbeapproximatedbyasingle-levelmulti-objectiveprogramming.Inaddition,thecorrespondinginterpolationfunctionsareupdatedsuchthatthesefunctionscanapproximatethelowerle
4、velsolutionfunctionverywell.Finally,themulti-objectiveprogrammingissolvedforobtaininganoptimalsolutionsetoftheoriginalproblem.Thesimulationontwoexamplesindicatestheproposedalgorithmiseffectiveandfeasible.Keywords:multi-objectivebilevelprogramming,geneticalgorithm
5、,interpolation.1.IntroductionBilevelprogrammingproblem(BLPP)isahierarchicaloptimizationproblem,whichincludesanupperlevelsdecisionmakerandalowerlevelsdecisionmaker.Bothofthemhavetheobjectivefunctionsandconstraintconditions.ThisproblemwasproposedbyStackelberg[1],an
6、dknownasStackelbergproblem.Themathematicalmodelofthiskindofproblemscanbewrittenasfollows:(1)Wherearedecisionvariables,areobjectivefunctionsandareconstraintfunctions;aretheothersconstraint,suchasupperandlowerboundsorintegerconstraints.Bilevelprogrammingproblemsocc
7、urinvariousapplications,suchaseconomicsandmanagement[2],engineering[3],transportationandothers.Mostofthesemodelsarebilevelsingleobjectiveproblems.Infact,therearelotsofreal-worldproblemsthatcanbemodeledasmulti-objectivebilevelprogrammingproblems[4].Inamulti-object
8、ivebilevelproblematleastonedecisionmakerhasmorethanoneobjectivefunction,andtheseobjectivesconflictwitheachother.Inrecentyears,multi-objectivebilevelprogramming
