DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

Jean Bigeon (), Sébastien Le Digabel () and Ludovic Salomon ()
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Jean Bigeon: GERAD and Département de mathématiques et génie industriel
Sébastien Le Digabel: GERAD and Département de mathématiques et génie industriel
Ludovic Salomon: GERAD and Département de mathématiques et génie industriel

Computational Optimization and Applications, 2021, vol. 79, issue 2, No 3, 338 pages

Abstract: Abstract The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to multiobjective derivative-free optimization with bound constraints. This method does not aggregate objectives and keeps a list of non dominated points which converges to a (local) Pareto set as long as the algorithm unfolds. As in the single-objective optimization MADS algorithm, this method is built around a search step and a poll step. Under classical direct search assumptions, it is proved that the so-called DMulti-MADS algorithm generates multiple subsequences of iterates which converge to a set of local Pareto stationary points. Finally, computational experiments suggest that this approach is competitive compared to the state-of-the-art algorithms for multiobjective blackbox optimization.

Keywords: Multiobjective optimization; Derivative-free optimization; Blackbox optimization; Mesh adaptive direct search; Clarke analysis. (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10589-021-00272-9

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