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Variable-sized uncertainty and inverse problems in robust optimization

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  • Chassein, André
  • Goerigk, Marc

Abstract

In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at finding a set of robust solutions that covers all possible uncertainty set outcomes. We refer to these problems as robust optimization with variable-sized uncertainty. We discuss how to construct smallest possible sets of min–max robust solutions and give bounds on their size.

Suggested Citation

  • Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    • Handle: RePEc:eee:ejores:v:264:y:2018:i:1:p:17-28
    DOI: 10.1016/j.ejor.2017.06.042
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    References listed on IDEAS

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    1. André Chassein & Marc Goerigk, 2016. "Performance Analysis in Robust Optimization," International Series in Operations Research & Management Science, in: Michael Doumpos & Constantin Zopounidis & Evangelos Grigoroudis (ed.), Robustness Analysis in Decision Aiding, Optimization, and Analytics, chapter 0, pages 145-170, Springer.
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    5. Chassein, André B. & Goerigk, Marc, 2015. "A new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 739-747.
    6. Chassein, André & Goerigk, Marc, 2017. "Minmax regret combinatorial optimization problems with ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 258(1), pages 58-69.
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    8. Nguyen, Kien Trung & Chassein, André, 2015. "The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance," European Journal of Operational Research, Elsevier, vol. 247(3), pages 774-781.
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    Cited by:

    1. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    2. Chan, Timothy C.Y. & Kaw, Neal, 2020. "Inverse optimization for the recovery of constraint parameters," European Journal of Operational Research, Elsevier, vol. 282(2), pages 415-427.
    3. Chassein, André & Goerigk, Marc, 2018. "Compromise solutions for robust combinatorial optimization with variable-sized uncertainty," European Journal of Operational Research, Elsevier, vol. 269(2), pages 544-555.
    4. Nguyen, Kien Trung & Hung, Nguyen Thanh, 2021. "The minmax regret inverse maximum weight problem," Applied Mathematics and Computation, Elsevier, vol. 407(C).

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