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Combining Cross-Entropy and MADS Methods for Inequality Constrained Global Optimization

Author

Listed:
  • Charles Audet

    (École Polytechnique de Montréal)

  • Jean Bigeon

    (LS2N)

  • Romain Couderc

    (École Polytechnique de Montréal
    Univ. Grenoble Alpes, CNRS, Grenoble INP)

Abstract

This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm with the Cross-Entropy (CE) method for nonsmooth constrained optimization. The CE method is used as an exploration step by the MADS algorithm. The result of this combination retains the convergence properties of MADS and allows an efficient exploration in order to move away from local minima. The CE method samples trial points according to a multivariate normal distribution whose mean and standard deviation are calculated from the best points found so far. Numerical experiments show the efficiency of this method compared to other global optimization heuristics. Moreover, applied on complex engineering test problems, this method allows an important improvement to reach the feasible region and to escape local minima.

Suggested Citation

  • Charles Audet & Jean Bigeon & Romain Couderc, 2021. "Combining Cross-Entropy and MADS Methods for Inequality Constrained Global Optimization," SN Operations Research Forum, Springer, vol. 2(3), pages 1-26, September.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:3:d:10.1007_s43069-021-00075-y
    DOI: 10.1007/s43069-021-00075-y
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    References listed on IDEAS

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    1. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    2. Charles Audet & Christophe Tribes, 2018. "Mesh-based Nelder–Mead algorithm for inequality constrained optimization," Computational Optimization and Applications, Springer, vol. 71(2), pages 331-352, November.
    3. Dirk P. Kroese & Sergey Porotsky & Reuven Y. Rubinstein, 2006. "The Cross-Entropy Method for Continuous Multi-Extremal Optimization," Methodology and Computing in Applied Probability, Springer, vol. 8(3), pages 383-407, September.
    4. Charles Audet & Michael Kokkolaras & Sébastien Le Digabel & Bastien Talgorn, 2018. "Order-based error for managing ensembles of surrogates in mesh adaptive direct search," Journal of Global Optimization, Springer, vol. 70(3), pages 645-675, March.
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