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Convergence of stochastic search algorithms to finite size Pareto set approximations

Abstract : In this work we investigate the convergence of stochastic search algorithms toward the Pareto set of continuous multi-objective optimization problems. The focus is on obtaining a finite approximation that should capture the entire solution set in a suitable sense, which will be defined using the concept of ε-dominance. Under mild assumptions about the process to generate new candidate solutions, the limit approximation set will be determined entirely by the archiving strategy. We propose and analyse two different archiving strategies which lead to a different limit behavior of the algorithms, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting Pareto set approximation.
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Submitted on : Friday, June 21, 2013 - 3:26:14 PM
Last modification on : Thursday, January 20, 2022 - 5:27:50 PM

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Oliver Schutze, Marco Laumanns, Carlos A. Coello Coello, El-Ghazali Talbi, Michael Dellnitz. Convergence of stochastic search algorithms to finite size Pareto set approximations. Journal of Global Optimization, 2008, 41 (4), pp.559-577. ⟨10.1007/s10898-007-9265-7⟩. ⟨hal-00836827⟩



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