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Handling of constraints in multiobjective blackbox optimization

Author

Listed:
  • Jean Bigeon

    (Nantes Université
    Group for Research in Decision Analysis, GERAD)

  • Sébastien Le Digabel

    (Polytechnique Montréal
    Group for Research in Decision Analysis, GERAD)

  • Ludovic Salomon

    (Polytechnique Montréal
    Group for Research in Decision Analysis, GERAD)

Abstract

This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where the search for a feasible point is prioritized if not available before improving the current solution set, or in a progressive barrier approach, where any trial point whose constraint violation function values are above a threshold are rejected. This threshold is progressively decreased along the iterations. As in the single-objective case, it is proved that these two variants generate feasible and/or infeasible sequences which converge either in the feasible case to a set of local Pareto optimal points or in the infeasible case to Clarke stationary points according to the constraint violation function. Computational experiments show that these two approaches are competitive with other state-of-the-art algorithms.

Suggested Citation

  • Jean Bigeon & Sébastien Le Digabel & Ludovic Salomon, 2024. "Handling of constraints in multiobjective blackbox optimization," Computational Optimization and Applications, Springer, vol. 89(1), pages 69-113, September.
    • Handle: RePEc:spr:coopap:v:89:y:2024:i:1:d:10.1007_s10589-024-00588-2
    DOI: 10.1007/s10589-024-00588-2
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    References listed on IDEAS

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    1. Charles Audet & Andrew R. Conn & Sébastien Le Digabel & Mathilde Peyrega, 2018. "A progressive barrier derivative-free trust-region algorithm for constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 307-329, November.
    2. Charles Audet & J. Dennis & Sébastien Digabel, 2010. "Globalization strategies for Mesh Adaptive Direct Search," Computational Optimization and Applications, Springer, vol. 46(2), pages 193-215, June.
    3. Paul Feliot & Julien Bect & Emmanuel Vazquez, 2017. "A Bayesian approach to constrained single- and multi-objective optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 97-133, January.
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