Stochastic radialbasisfunctionalgorithmsforlarge-scaleoptimization involving expensiveblack-boxobjectiveandconstraintfunctions

This paperpresentsanewalgorithmforderivative-freeoptimizationofexpensiveblack-boxobjective functionssubjecttoexpensiveblack-boxinequalityconstraints.Theproposedalgorithm,called ConstrLMSRBF,usesradialbasisfunction(RBF)surrogatemodelsandisanextensionoftheLocalMetric StochasticRBF(LMSRBF)algorithmbyRegisandShoemaker(2007a) [1] that canhandleblack-box inequalityconstraints.Previousalgorithmsfortheoptimizationofexpensivefunctionsusingsurrogate modelshavemostlydealtwithboundconstrainedproblemswhereonlytheobjectivefunctionis expensive,andso,thesurrogatemodelsareusedtoapproximatetheobjectivefunctiononly.In contrast,ConstrLMSRBFbuildsRBFsurrogatemodelsfortheobjectivefunctionandalsoforallthe constraintfunctionsineachiteration,andusestheseRBFmodelstoguidetheselectionofthenextpoint wheretheobjectiveandconstraintfunctionswillbeevaluated.Computationalresultsindicatethat ConstrLMSRBFisbetterthanalternativemethodson9outof14testproblemsandontheMOPTA08 problemfromtheautomotiveindustry(Jones,2008 [2]). TheMOPTA08problemhas124decision variablesand68inequalityconstraintsandisconsideredalarge-scaleproblemintheareaofexpensive black-boxoptimization.ThealternativemethodsincludeaMeshAdaptiveDirectSearch(MADS) algorithm(AbramsonandAudet,2006 [3]; AudetandDennis,2006 [4]) thatusesakriging-based surrogatemodel,theMultistartLMSRBFalgorithmbyRegisandShoemaker(2007a) [1] modifiedto handle black-boxconstraintsviaapenaltyapproach,ageneticalgorithm,apatternsearchalgorithm,a sequentialquadraticprogrammingalgorithm,andCOBYLA(Powell,1994 [5]), whichisaderivative-free trust-regionalgorithm.Basedontheresultsofthisstudy,theresultsinJones(2008) [2] and other approachespresentedattheISMP2009conference,ConstrLMSRBFappearstobeamongthebest,ifnot the best,knownalgorithmfortheMOPTA08probleminthesenseofprovidingthemostimprovement from aninitialfeasiblesolutionwithinaverylimitednumberofobjectiveandconstraintfunction evaluations.