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Globally convergent evolution strategies for constrained optimization

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  • Y. Diouane
  • S. Gratton
  • L. Vicente

Abstract

In this paper we propose, analyze, and test algorithms for constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, feasibility is first enforced by a barrier function and the objective function is then evaluated directly at the feasible generated points. A second approach projects first all the generated points onto the feasible domain before evaluating the objective function. The resulting algorithms enjoy favorable global convergence properties (convergence to stationarity from arbitrary starting points), regardless of the linearity of the constraints. The algorithmic implementation (i) includes a step where previously evaluated points are used to accelerate the search (by minimizing quadratic models) and (ii) addresses the particular cases of bounds on the variables and linear constraints. Our solver is compared to others, and the numerical results confirm its competitiveness in terms of efficiency and robustness. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Y. Diouane & S. Gratton & L. Vicente, 2015. "Globally convergent evolution strategies for constrained optimization," Computational Optimization and Applications, Springer, vol. 62(2), pages 323-346, November.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:2:p:323-346
    DOI: 10.1007/s10589-015-9747-3
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    References listed on IDEAS

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    1. L. Ingber & B. Rosen, 1992. "Genetic algorithms and very fast simulated reannealing: A comparison," Lester Ingber Papers 92ga, Lester Ingber.
    2. Luis Rios & Nikolaos Sahinidis, 2013. "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, Springer, vol. 56(3), pages 1247-1293, July.
    3. A. Custódio & H. Rocha & L. Vicente, 2010. "Incorporating minimum Frobenius norm models in direct search," Computational Optimization and Applications, Springer, vol. 46(2), pages 265-278, June.
    4. I. D. Coope & C. J. Price, 2000. "Frame Based Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 261-274, November.
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    Cited by:

    1. Youssef Diouane & Victor Picheny & Rodolophe Le Riche & Alexandre Scotto Di Perrotolo, 2023. "TREGO: a trust-region framework for efficient global optimization," Journal of Global Optimization, Springer, vol. 86(1), pages 1-23, May.
    2. S. Gratton & C. W. Royer & L. N. Vicente & Z. Zhang, 2019. "Direct search based on probabilistic feasible descent for bound and linearly constrained problems," Computational Optimization and Applications, Springer, vol. 72(3), pages 525-559, April.

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