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1、Comput.MethodsAppl.Mech.Engrg.196(2007)3190–3218www.elsevier.com/locate/cmaRobustoptimization–Acomprehensivesurveya,*bHans-GeorgBeyer,BernhardSendhoffaVorarlbergUniversityofAppliedSciences,Dornbirn,AustriabHondaResearchInstituteEuropeGmbH,Offenbach,GermanyReceived4Septe
2、mber2006;receivedinrevisedform28February2007;accepted4March2007AbstractThispaperreviewsthestate-of-the-artinrobustdesignoptimization–thesearchfordesignsandsolutionswhichareimmunewithrespecttoproductiontolerances,parameterdriftsduringoperationtime,modelsensitivitiesand
3、others.StartingwithashortglimpsofTaguchi’srobustdesignmethodology,adetailedsurveyofapproachestorobustoptimizationispresented.Thisincludesadetaileddis-cussiononhowtoaccountfordesignuncertaintiesandhowtomeasurerobustness(i.e.,howtoevaluaterobustness).Themainfocuswillbeo
4、nthedifferentapproachestoperformrobustoptimizationinpracticeincludingthemethodsofmathematicalprogramming,deter-ministicnonlinearoptimization,anddirectsearchmethodssuchasstochasticapproximationandevolutionarycomputation.Itdiscussesthestrengthsandweaknessesofthedifferentm
5、ethods,thus,providingabasisforguidingtheengineertothemostappropriatetech-niques.Italsoaddressesperformanceaspectsandtestscenariosfordirectrobustoptimizationtechniques.Ó2007ElsevierB.V.Allrightsreserved.Keywords:Directsearchmethods;Evolutionarycomputation;Handlingdesig
6、nuncertainties;Mathematicalprogramming;Noisyoptimization;Robustdesign;Robustoptimization1.Introductionaccountfordesignconstraintsimposedonthedesignparametersx.Suchconstraintscanbemodeledbyinequal-Inordertodesignandmanufacturehighqualityprod-itiesand/orequalitiesrestri
7、ctingthedesignspace(searchuctsataminimumofcosts,techniquesareneededwhichspace).Inmathematicaltermsageneraloptimizationtaskareabletofindthosedesignswhichmeettherequirementscanbestatedasusuallyspecifiedbyobjectives(goalfunctions)atthebegin-9optimize:fðxÞ;ðaÞ>=ningofthedes
8、ignprocess.Providedthatthegeneralsystemdesignhasbeenfixed(e.g.,thetypeofproductanditssubjectto:giðxÞ60;i¼1;...;I;ðbÞð1Þ>;desi
