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A double oracle approach to minmax regret optimization problems with interval data

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  • Gilbert, Hugo
  • Spanjaard, Olivier

Abstract

In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk (2015). This lower bound can be viewed as the optimal value of a linear programming relaxation of a mixed integer programming formulation of minmax regret optimization, but the contribution of the paper is to compute this lower bound via a double oracle algorithm (McMahan, Gordon, & Blum, 2003) that we specify. The double oracle algorithm is designed by relying on a game theoretic view of robust optimization, similar to the one developed by Mastin, Jaillet, and Chin (2015), and it can be efficiently implemented for any minmax regret optimization problem whose standard version is “easy”. We describe how to efficiently embed this lower bound in a branch and bound procedure. Finally we apply our approach to the robust shortest path problem. Our numerical results show a significant gain in the computation times compared to previous approaches in the literature.

Suggested Citation

  • Gilbert, Hugo & Spanjaard, Olivier, 2017. "A double oracle approach to minmax regret optimization problems with interval data," European Journal of Operational Research, Elsevier, vol. 262(3), pages 929-943.
    • Handle: RePEc:eee:ejores:v:262:y:2017:i:3:p:929-943
    DOI: 10.1016/j.ejor.2017.04.058
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    References listed on IDEAS

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    1. 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.
    2. 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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    Cited by:

    1. Luo, Chunling & Tan, Chin Hon & Liu, Xiao, 2020. "Maximum excess dominance: Identifying impractical solutions in linear problems with interval coefficients," European Journal of Operational Research, Elsevier, vol. 282(2), pages 660-676.
    2. Schroeder, Pascal & Kacem, Imed, 2020. "Competitive difference analysis of the cash management problem with uncertain demands," European Journal of Operational Research, Elsevier, vol. 283(3), pages 1183-1192.

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