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1、Multi-ObjectiveGeneticAlgorithms:ProblemDifficultiesandConstructionofTestProblemsKalyanmoyDebKanpurGeneticAlgorithmsLaboratory(KanGAL)DepartmentofMechanicalEngineeringIndianInstituteofTechnologyKanpurKanpur,PIN208016,IndiaE-mail:deb@iitk.ac.inAbstractInthispaper,westudytheprobl
2、emfeaturesthatmaycauseamulti-objectivegeneticalgorithm(GA)difficultytoconvergetothetruePareto-optimalfront.Identificationofsuchfeatureshelpsusdevelopdifficulttestproblemsformulti-objectiveoptimization.Multi-objectivetestproblemsareconstructedfromsingle-objectiveoptimizationproble
3、ms,therebyallowingknowndifficultfeaturesofsingle-objectiveproblems(suchasmulti-modalityordeception)tobedirectlytransferredtothecorrespondingmulti-objectiveproblem.Inaddition,testproblemshavingfeaturesspecifictomulti-objectiveoptimizationarealsoconstructed.Theconstructionmethodol
4、ogyallowsasimplerwaytodeveloptestproblemshavingotherdifficultandinterestingproblemfeatures.Moreimportantly,thesedifficulttestproblemswillenableresearcherstotesttheiralgorithmsforspecificaspectsofmulti-objectiveoptimizationinthecomingyears.1IntroductionAfteraboutadecadesincethepio
5、neeringworkbySchaffer(1984;1985),anumberofstudiesonmulti-objectivegeneticalgorithms(GAs)havebeenpursuedsincetheyear1994,althoughmostofthesestudiestookahintfromGoldberg(1989).TheprimaryreasonforthesestudiesisauniquefeatureofGAs—populationapproach—thatmakethemhighlysuitabletobeu
6、sedinmulti-objectiveoptimization.SinceGAsworkwithapopulationofsolutions,multiplePareto-optimalsolutionscanbecapturedinaGApopu-lationinasinglesimulationrun.Duringtheyear1993-94,anumberofindependentGAimplementations(FonsecaandFleming,1993;Horn,Nafploitis,andGoldberg,1994;Sriniva
7、sandDeb,1994)emerged.Later,anumberofotherresearchershaveusedtheseimplementationsinvariousmulti-objectiveoptimiza-tionapplicationswithsuccess(Cunha,Oliviera,andCovas,1997;Eheart,Cieniawski,andRanjithan,1993;Mitra,Deb,andGupta,1998;ParksandMiller,1998;Weile,Michelsson,andGoldber
8、g,1996).Anumberofstudieshavealsoconcentratedindevelopingnewan
