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dc.contributor.authorLovison, Alberto
dc.contributor.authorMiettinen, Kaisa
dc.date.accessioned2020-09-07T12:16:53Z
dc.date.available2020-09-07T12:16:53Z
dc.date.issued2021
dc.identifier.citationLovison, A., & Miettinen, K. (2021). On the Extension of the DIRECT Algorithm to Multiple Objectives. <i>Journal of Global Optimization</i>, <i>79</i>(2), 387-412. <a href="https://doi.org/10.1007/s10898-020-00942-8" target="_blank">https://doi.org/10.1007/s10898-020-00942-8</a>
dc.identifier.otherCONVID_41946198
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/71664
dc.description.abstractDeterministic global optimization algorithms like Piyavskii–Shubert, DIRECT, EGO and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce representations of the globally Pareto optimal set are usually based on heuristics. We analyze the concept of global convergence for multiobjective optimization algorithms and propose a convergence criterion based on the Hausdorff distance in the decision space. Under this light, we consider the well-known global optimization algorithm DIRECT, analyze the available algorithms in the literature that extend DIRECT to multiple objectives and discuss possible alternatives. In particular, we propose a novel definition for the notion of potential Pareto optimality extending the notion of potential optimality defined in DIRECT. We also discuss its advantages and disadvantages when compared with algorithms existing in the literature.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherSpringer Science and Business Media LLC
dc.relation.ispartofseriesJournal of Global Optimization
dc.rightsCC BY 4.0
dc.subject.otherglobal convergence
dc.subject.othermultiobjective optimization
dc.subject.othermultiple criteria optimization
dc.subject.otherDIRECT algorithm
dc.subject.otherdeterministic optimization algorithms
dc.titleOn the Extension of the DIRECT Algorithm to Multiple Objectives
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202009075773
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.contributor.oppiaineTietotekniikkafi
dc.contributor.oppiaineMultiobjective Optimization Groupfi
dc.contributor.oppiaineLaskennallinen tiedefi
dc.contributor.oppiaineMathematical Information Technologyen
dc.contributor.oppiaineMultiobjective Optimization Groupen
dc.contributor.oppiaineComputational Scienceen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange387-412
dc.relation.issn0925-5001
dc.relation.numberinseries2
dc.relation.volume79
dc.type.versionpublishedVersion
dc.rights.copyright© The Author(s) 2020
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber287496
dc.subject.ysomonitavoiteoptimointi
dc.subject.ysodeterminantit
dc.subject.ysomonimuuttujamenetelmät
dc.subject.ysooptimointi
dc.subject.ysoalgoritmit
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p32016
jyx.subject.urihttp://www.yso.fi/onto/yso/p11285
jyx.subject.urihttp://www.yso.fi/onto/yso/p2131
jyx.subject.urihttp://www.yso.fi/onto/yso/p13477
jyx.subject.urihttp://www.yso.fi/onto/yso/p14524
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1007/s10898-020-00942-8
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundinginformationOpen access funding provided by Universitá degli Studi di Padova within the CRUI-CARE Agreement.
dc.type.okmA1


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