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Multipolar robust optimization

Author

Listed:
  • Walid Ben-Ameur

    (Université Paris-Saclay)

  • Adam Ouorou

    (Orange Labs Research)

  • Guanglei Wang

    (Université Paris-Saclay
    Orange Labs Research)

  • Mateusz Żotkiewicz

    (Warsaw University of Technology)

Abstract

We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully Adjustable Robust Counterpart. It consists in selecting a set of poles whose convex hull contains some projection of the uncertainty set, and computing a recourse strategy for each data scenario as a convex combination of some optimized recourses (one for each pole). We show that the proposed multipolar robust counterpart is tractable and its complexity is controllable. Further, we show that under some mild assumptions, two sequences of upper and lower bounds converge to the optimal value of the fully adjustable robust counterpart. We numerically investigate a couple of applications in the literature demonstrating that the approach can effectively improve the affinely adjustable policy.

Suggested Citation

  • Walid Ben-Ameur & Adam Ouorou & Guanglei Wang & Mateusz Żotkiewicz, 2018. "Multipolar robust optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(4), pages 395-434, December.
    • Handle: RePEc:spr:eurjco:v:6:y:2018:i:4:d:10.1007_s13675-017-0092-4
    DOI: 10.1007/s13675-017-0092-4
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    References listed on IDEAS

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