Evolutionary multiobjectiveoptimizationusinganoutranking-baseddominance generalization

One aspectthatisoftendisregardedinthecurrentresearchonevolutionarymultiobjectiveoptimization is thefactthatthesolutionofamultiobjectiveoptimizationprobleminvolvesnotonlythesearchitself, but alsoadecisionmakingprocess.Mostcurrentapproachesconcentrateonadaptinganevolutionary algorithm togeneratetheParetofrontier.Inthiswork,wepresentanewideatoincorporatepreferences into amulti-objectiveevolutionaryalgorithm(MOEA).Weintroduceabinaryfuzzypreferencerelation that expressesthedegreeoftruthofthepredicate“x is atleastasgoodas y”. Onthisbasis,astrict preference relationwithareasonablyhighdegreeofcredibilitycanbeestablishedonanypopulation. An alternative x is notstrictlyoutrankedifandonlyiftheredoesnotexistanalternative y which is strictly preferredto x. Itiseasytoprovethatthebestsolutionisnotstrictlyoutranked.Forvalidating our proposedapproach,weusedthenon-dominatedsortinggeneticalgorithmII(NSGA-II),butreplacing Pareto dominancebytheabovenon-outrankedconcept.So,wesearchforthenon-strictlyoutranked frontier thatisasubsetoftheParetofrontier.Inseveralinstancesofanine-objectiveknapsackproblem our proposalclearlyoutperformsthestandardNSGA-II,achievingnon-outrankedsolutionswhicharein an obviouslyprivilegedzoneoftheParetofrontier.