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

Author

Listed:
  • Jean Bigeon

    (GERAD and Département de mathématiques et génie industriel
    CNRS, LS2N)

  • Sébastien Le Digabel

    (GERAD and Département de mathématiques et génie industriel)

  • Ludovic Salomon

    (GERAD and Département de mathématiques et génie industriel)

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.

Suggested Citation

  • Jean Bigeon & Sébastien Le Digabel & Ludovic Salomon, 2021. "DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 301-338, June.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:2:d:10.1007_s10589-021-00272-9
    DOI: 10.1007/s10589-021-00272-9
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    References listed on IDEAS

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    1. Audet, Charles & Savard, Gilles & Zghal, Walid, 2010. "A mesh adaptive direct search algorithm for multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 545-556, August.
    2. G. Cocchi & G. Liuzzi & A. Papini & M. Sciandrone, 2018. "An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints," Computational Optimization and Applications, Springer, vol. 69(2), pages 267-296, March.
    3. Sergeyev, Yaroslav D. & Kvasov, Dmitri E. & Mukhametzhanov, Marat S., 2017. "Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 96-109.
    4. A. L. Custódio & J. F. A. Madeira, 2018. "MultiGLODS: global and local multiobjective optimization using direct search," Journal of Global Optimization, Springer, vol. 72(2), pages 323-345, October.
    5. Audet, Charles & Bigeon, Jean & Cartier, Dominique & Le Digabel, Sébastien & Salomon, Ludovic, 2021. "Performance indicators in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 292(2), pages 397-422.
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