Stochastic convergence of random search methods to fixed size Pareto front approximations

Marco Laumanns and Rico Zenklusen

European Journal of Operational Research, 2011, vol. 213, issue 2, 414-421

Abstract: In this paper we investigate to what extent random search methods, equipped with an archive of bounded size to store a limited amount of solutions and other data, are able to obtain good Pareto front approximations. We propose and analyze two archiving schemes that allow for maintaining a sequence of solution sets of given cardinality that converge with probability one to an [epsilon]-Pareto set of a certain quality, under very mild assumptions on the process used to sample new solutions. The first algorithm uses a hierarchical grid to define a family of approximate dominance relations to compare solutions and solution sets. Acceptance of a new solution is based on a potential function that counts the number of occupied boxes (on various levels) and thus maintains a strictly monotonous progress to a limit set that covers the Pareto front with non-overlapping boxes at finest resolution possible. The second algorithm uses an adaptation scheme to modify the current value of [epsilon] based on the information gathered during the run. This way it will be possible to achieve convergence to the best (smallest) [epsilon] value, and to a corresponding solution set of k solutions that [epsilon]-dominate all other solutions, which is probably the best possible result regarding the limit behavior of random search methods or metaheuristics for obtaining Pareto front approximations.

Keywords: Multiple; criteria; analysis; Multiobjective; optimization; Metaheuristics; Search; theory (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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