Survey of multi-objective optimization methods for engineering

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1、ReviewarticleStructMultidiscOptim26,369–395(2004)DOI10.1007/s00158-003-0368-6Surveyofmulti-objectiveoptimizationmethodsforengineeringR.T.MarlerandJ.S.AroraAbstractAsurveyofcurrentcontinuousnonlinearmulti-FnormNormalizedobjectivefunctionsiobjectiveoptimization(MOO)conc

2、eptsandmethodsisFsPrimaryobjectivefunctionpresented.Itconsolidatesandrelatesseeminglydiffer-FtransTransformedobjectivefunctionsientterminologyandmethods.ThemethodsaredividedF◦Utopiapointintothreemajorcategories:methodswithaprioriar-FVectorofobjectivefunctions(pointinth

3、ecriterionticulationofpreferences,methodswithaposterioriar-space)ticulationofpreferences,andmethodswithnoarticula-gjInequalityconstraintstionofpreferences.GeneticalgorithmsaresurveyedashlEqualityconstraintswell.Commentaryisprovidedonthreefronts,concern-kNumberofobject

4、ivefunctionsingtheadvantagesandpitfallsofindividualmethods,λMin-maxparameterthedifferentclassesofmethods,andthefieldofMOOmNumberofinequalityconstraintsasawhole.TheCharacteristicsofthemostsignificantnNumberofdesignvariablesmethodsaresummarized.Conclusionsaredrawnthatre-pE

5、xponentforaglobalcriterionflectoften-neglectedideasandapplicabilitytoengineer-UUtilityfunctioningproblems.Itisfoundthatnosingleapproachissupe-wVectorofweightingcoefficients/exponentsrior.Rather,theselectionofaspecificmethoddependsonxVectorofdesignvariables(pointinthedesig

6、nspace)thetypeofinformationthatisprovidedintheproblem,XFeasibledesignspacetheuser’spreferences,thesolutionrequirements,andthezAspirationpointavailabilityofsoftware.ZFeasiblecriterionspaceKeywordsoptimization,multi-objective,multi-criteria,engineering1Introduction1.1Ba

7、ckgroundandobjectivesListofkeysymbolsTheprocessofoptimizingsystematicallyandsimultan-eNumberofequalityconstraintseouslyacollectionofobjectivefunctionsiscalledmulti-FgGlobalcriterionfunctionobjectiveoptimization(MOO)orvectoroptimization.FmaxMaximumobjectivefunctionvalu

8、esThispaperisasurveyofmethodsforMOOandisacon-idensationoftheworkbyMarlerandArora(2003),whichReceived:25September2002provided