{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T15:53:09Z","timestamp":1726847589758},"reference-count":19,"publisher":"MIT Press - Journals","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Evolutionary Computation"],"published-print":{"date-parts":[[2010,3]]},"abstract":" Recently, 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 \u025b-dominance. Though bounds on the quality of the limit approximation\u2014which are entirely determined by the archiving strategy and the value of \u025b\u2014have 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 \u2208 A, is \u201clarge.\u201d 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\u2014multi-objective continuation methods\u2014by showing that the concept of \u025b-dominance can be integrated into this approach in a suitable way. <\/jats:p>","DOI":"10.1162\/evco.2010.18.1.18103","type":"journal-article","created":{"date-parts":[[2010,1,11]],"date-time":"2010-01-11T17:31:37Z","timestamp":1263231097000},"page":"65-96","source":"Crossref","is-referenced-by-count":53,"title":["Computing Gap Free Pareto Front Approximations with Stochastic Search Algorithms"],"prefix":"10.1162","volume":"18","author":[{"given":"Oliver","family":"Sch\u00fctze","sequence":"first","affiliation":[{"name":"CINVESTAV-IPN, Departamento de Computaci\u00f3n, M\u00e9xico D.F. 07360, M\u00e9xico."}]},{"given":"Marco","family":"Laumanns","sequence":"additional","affiliation":[{"name":"Institute for Operations Research, ETH Z\u00fcrich, 8092, Z\u00fcrich, Switzerland."}]},{"given":"Emilia","family":"Tantar","sequence":"additional","affiliation":[{"name":"INRIA Bordeaux Sud-Ouest, Institut de Math\u00e9matiques de Bordeaux, 33405 Talence Cedex, France."}]},{"given":"Carlos A. Coello","family":"Coello","sequence":"additional","affiliation":[{"name":"CINVESTAV-IPN, Departamento de Computaci\u00f3n, M\u00e9xico D.F. 07360, M\u00e9xico."}]},{"given":"El-Ghazali","family":"Talbi","sequence":"additional","affiliation":[{"name":"INRIA Lille Nord Europe, Parc Scientifique de la Haute Borne, 59650, Villeneuve d\u2032Ascq, France."},{"name":"Visiting Professor in King Saud University, Saudi Arabia."}]}],"member":"281","reference":[{"issue":"1","key":"p_2","first-page":"3","volume":"6","author":"Brown M.","year":"2005","journal-title":"International Journal on Computers, Systems, and Signals"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1162\/106365605774666895"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/s001860300316"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(98)00262-8"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1162\/106365600568167"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2003.810755"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1162\/106365602760234108"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00936165"},{"issue":"3","key":"p_17","first-page":"275","volume":"26","author":"Rudolph G.","year":"1997","journal-title":"Control and Cybernetics"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1109\/4235.687885"},{"key":"p_19","doi-asserted-by":"crossref","first-page":"67","DOI":"10.3233\/FI-1998-35123405","volume":"35","author":"Rudolph G.","year":"1998","journal-title":"Fundamenta Informaticae"},{"key":"p_21","first-page":"36","volume":"2007","author":"Rudolph G.","year":"2007","journal-title":"EMO"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1007\/BF02247962"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1007\/s101070050128"},{"key":"p_25","doi-asserted-by":"publisher","DOI":"10.1080\/03052150701821328"},{"key":"p_30","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-007-9265-7"},{"key":"p_34","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(97)00056-8"},{"key":"p_35","doi-asserted-by":"publisher","DOI":"10.1007\/s10009-008-0066-1"},{"key":"p_37","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2003.810758"}],"container-title":["Evolutionary Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/evco.2010.18.1.18103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:57:48Z","timestamp":1615586268000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/evco\/article\/18\/1\/65-96\/1334"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["10.1162\/evco.2010.18.1.18103"],"URL":"https:\/\/doi.org\/10.1162\/evco.2010.18.1.18103","relation":{},"ISSN":["1063-6560","1530-9304"],"issn-type":[{"value":"1063-6560","type":"print"},{"value":"1530-9304","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,3]]}}}