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Globalized Robust Optimization for Nonlinear Uncertain Inequalities

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  • Ben-Tal, A.
  • Brekelmans, Ruud

    (Tilburg University, School of Economics and Management)

  • den Hertog, Dick

    (Tilburg University, School of Economics and Management)

  • Vial, J.P.

Abstract

Robust optimization is a methodology that can be applied to problems that are affected by uncertainty in their parameters. The classical robust counterpart of a problem requires the solution to be feasible for all uncertain parameter values in a so-called uncertainty set and offers no guarantees for parameter values outside this uncertainty set. The globalized robust counterpart (GRC) extends this idea by allowing controlled constraint violations in a larger uncertainty set. The constraint violations are controlled by the distance of the parameter from the original uncertainty set. We derive tractable GRCs that extend the initial GRCs in the literature: our GRC is applicable to nonlinear constraints instead of only linear or conic constraints, and the GRC is more flexible with respect to both the uncertainty set and distance measure function, which are used to control the constraint violations. In addition, we present a GRC approach that can be used to provide an extended trade-off overview between the objective value and several robustness measures.
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Suggested Citation

  • Ben-Tal, A. & Brekelmans, Ruud & den Hertog, Dick & Vial, J.P., 2015. "Globalized Robust Optimization for Nonlinear Uncertain Inequalities," Other publications TiSEM 05c1b5b6-5b26-46f6-bd3a-a, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:05c1b5b6-5b26-46f6-bd3a-ade07f4c5f04
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    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
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    3. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    4. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    5. Evers, L. & Dollevoet, T.A.B. & Barros, A.I. & Monsuur, H., 2011. "Robust UAV Mission Planning," Econometric Institute Research Papers EI 2011-07, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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    7. Ben-Tal, A. & den Hertog, D. & Vial, J.P., 2012. "Deriving Robust Counterparts of Nonlinear Uncertain Inequalities," Discussion Paper 2012-053, Tilburg University, Center for Economic Research.
    8. Huan Xu & Constantine Caramanis & Shie Mannor, 2012. "Optimization Under Probabilistic Envelope Constraints," Operations Research, INFORMS, vol. 60(3), pages 682-699, June.
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    Cited by:

    1. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2022. "Robust portfolio selection problems: a comprehensive review," Operational Research, Springer, vol. 22(4), pages 3203-3264, September.
    2. Qinghe Sun & Li Chen & Mabel C. Chou & Qiang Meng, 2023. "Mitigating the financial risk behind emission cap compliance: A case in maritime transportation," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 283-300, January.
    3. Wang, Jinpei & Bai, Xuejie & Liu, Yankui, 2023. "Globalized robust bilevel optimization model for hazmat transport network design considering reliability," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    4. Feng Liu & Zhi Chen & Shuming Wang, 2023. "Globalized Distributionally Robust Counterpart," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1120-1142, September.
    5. Ernst Roos & Dick den Hertog, 2020. "Reducing Conservatism in Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1109-1127, October.
    6. Roos, Ernst & den Hertog, Dick, 2019. "Reducing conservatism in robust optimization," Other publications TiSEM ad0238cd-de7a-4366-b487-b, Tilburg University, School of Economics and Management.
    7. Alireza Ghahtarani & Ahmed Saif & Alireza Ghasemi, 2021. "Robust Portfolio Selection Problems: A Comprehensive Review," Papers 2103.13806, arXiv.org, revised Jan 2022.
    8. Shuming Wang & Yan-Fu Li & Tong Jia, 2020. "Distributionally Robust Design for Redundancy Allocation," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 620-640, July.

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