DEMORS:Ahybridmulti-objectiveoptimizationalgorithmusingdifferentialevolution and roughsettheoryforconstrainedproblems

The aimofthispaperistoshowhowthehybridizationofamulti-objectiveevolutionaryalgorithm (MOEA) andalocalsearchmethodbasedontheuseofroughsettheoryisaviablealternativetoobtaina robust algorithmabletosolvedifficultconstrainedmulti-objectiveoptimizationproblemsatamoderate computational cost.ThispaperextendsapreviouslypublishedMOEA[Hernández-DíazAG,Santana- Quintero LV,CoelloCoelloC,CaballeroR,MolinaJ.Anewproposalformulti-objectiveoptimizationusing differential evolutionandroughsettheory.In:2006geneticandevolutionarycomputationconference (GECCOʹ2006). Seattle,Washington,USA:ACMPress;July2006],whichwaslimitedtounconstrained multi-objective optimizationproblems.Here,themainideaistousethissortofhybridapproachto approximate theParetofrontofaconstrainedmulti-objectiveoptimizationproblemwhileperforminga relatively lownumberoffitnessfunctionevaluations.Sinceinreal-worldproblemsthecostofevaluating the objectivefunctionsisthemostsignificant,ourunderlyingassumptionisthat,byaimingtominimize the numberofsuchevaluations,ourMOEAcanbeconsideredefficient.Asinitspreviousversion,our hybrid approachoperatesintwostages:inthefirstone,amulti-objectiveversionofdifferentialevolution is usedtogenerateaninitialapproximationoftheParetofront.Then,inthesecondstage,roughset theory isusedtoimprovethespreadandqualityofthisinitialapproximation.Toassesstheperformance of ourproposedapproach,weadopt,ontheonehand,asetofstandardbi-objectiveconstrainedtest problems and,ontheotherhand,alargereal-worldproblemwitheightobjectivefunctionsand160 decision variables.Thefirstsetofproblemsaresolvedperforming10,000fitnessfunctionevaluations, which isacompetitivevaluecomparedtothenumberofevaluationspreviouslyreportedinthespecial- ized literatureforsuchproblems.Thereal-worldproblemissolvedperforming250,000fitnessfunction evaluations, mainlybecauseofitshighdimensionality.Ourresultsarecomparedwithrespecttothose generated byNSGA-II,whichisaMOEArepresentativeofthestate-of-the-artinthearea.