Convergence of stochastic search algorithms to finite size pareto set approximations

Authors:
Oliver Schütze;Marco Laumanns;Carlos A. Coello Coello;Michael Dellnitz;El-Ghazali Talbi
Affiliations:
Computer Science Department, CINVESTAV-IPN, Mexico City, Mexico 07300;Institute for Operations Research, ETH Zurich, Zurich, Switzerland 8092;Computer Science Department, CINVESTAV-IPN, Mexico City, Mexico 07300;Faculty for Computer Science, Electrical Engineering and Mathematics, Institute for Mathematics, University of Paderborn, Paderborn, Germany 33098;LIFL, CNRS Bât M3, Cité Scientifique, INRIA Futurs, Villeneuve d'Ascq, France 59655
Venue:
Journal of Global Optimization
Year:
2008

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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 驴-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.