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Computing gap-free Pareto front approximations with stochastic search algorithms

hal.structure.identifierCentro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional [CINVESTAV]
dc.contributor.authorSCHÜTZE, Oliver
hal.structure.identifierEidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] [ETH Zürich]
dc.contributor.authorLAUMANNS, Marco
hal.structure.identifierAdvanced Learning Evolutionary Algorithms [ALEA]
dc.contributor.authorTANTAR, Emilia
hal.structure.identifierCentro de Investigacion y de Estudios Avanzados del Instituto Politécnico Nacional [CINVESTAV]
dc.contributor.authorCOELLO COELLO, Carlos
hal.structure.identifierParallel Cooperative Multi-criteria Optimization [DOLPHIN]
dc.contributor.authorTALBI, El-Ghazali
dc.date.issued2010-03
dc.identifier.issn1063-6560
dc.description.abstractEnRecently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of ε-dominance. Though bounds on the quality of the limit approximation---which are entirely determined by the archiving strategy and the value of ε---have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a ∈ A, is “large.” Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy---multi-objective continuation methods---by showing that the concept of ε-dominance can be integrated into this approach in a suitable way.
dc.language.isoen
dc.publisherMassachusetts Institute of Technology Press (MIT Press)
dc.title.enComputing gap-free Pareto front approximations with stochastic search algorithms
dc.typeArticle de revue
dc.identifier.doi10.1162/evco.2010.18.1.18103
dc.subject.halInformatique [cs]/Recherche opérationnelle [cs.RO]
bordeaux.journalEvolutionary Computation
bordeaux.page65-96
bordeaux.volume18
bordeaux.issue1
bordeaux.peerReviewedoui
hal.identifierhal-00750950
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00750950v1
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