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Differential Evolution with Estimation of Distribution for Worst-Case Scenario Optimization

Author

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  • Margarita Antoniou

    (Computer Systems Department, Jožef Stefan Institute, Jamova c. 39, SI-1000 Ljubljana, Slovenia
    Jožef Stefan International Postgraduate School, Jamova c. 39, SI-1000 Ljubljana, Slovenia)

  • Gregor Papa

    (Computer Systems Department, Jožef Stefan Institute, Jamova c. 39, SI-1000 Ljubljana, Slovenia
    Jožef Stefan International Postgraduate School, Jamova c. 39, SI-1000 Ljubljana, Slovenia)

Abstract

Worst-case scenario optimization deals with the minimization of the maximum output in all scenarios of a problem, and it is usually formulated as a min-max problem. Employing nested evolutionary algorithms to solve the problem requires numerous function evaluations. This work proposes a differential evolution with an estimation of distribution algorithm. The algorithm has a nested form, where a differential evolution is applied for both the design and scenario space optimization. To reduce the computational cost, we estimate the distribution of the best worst solution for the best solutions found so far. The probabilistic model is used to sample part of the initial population of the scenario space differential evolution, using a priori knowledge of the previous generations. The method is compared with a state-of-the-art algorithm on both benchmark problems and an engineering application, and the related results are reported.

Suggested Citation

  • Margarita Antoniou & Gregor Papa, 2021. "Differential Evolution with Estimation of Distribution for Worst-Case Scenario Optimization," Mathematics, MDPI, vol. 9(17), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2137-:d:627794
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    References listed on IDEAS

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    1. Julien Marzat & Eric Walter & Hélène Piet-Lahanier, 2013. "Worst-case global optimization of black-box functions through Kriging and relaxation," Journal of Global Optimization, Springer, vol. 55(4), pages 707-727, April.
    2. Gorissen, Bram L. & Yanıkoğlu, İhsan & den Hertog, Dick, 2015. "A practical guide to robust optimization," Omega, Elsevier, vol. 53(C), pages 124-137.
    3. Fuqing Zhao & Zhongshi Shao & Junbiao Wang & Chuck Zhang, 2016. "A hybrid differential evolution and estimation of distribution algorithm based on neighbourhood search for job shop scheduling problems," International Journal of Production Research, Taylor & Francis Journals, vol. 54(4), pages 1039-1060, February.
    4. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
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