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Robust Discrete Optimization Under Discrete and Interval Uncertainty: A Survey

In: Robustness Analysis in Decision Aiding, Optimization, and Analytics

Author

Listed:
  • Adam Kasperski

    (Wrocław University of Technology)

  • Paweł Zieliński

    (Wrocław University of Technology)

Abstract

In this chapter a review of recent results on robust discrete optimization is presented. The most popular discrete and interval uncertainty representations are discussed. Various robust concepts are presented, namely the traditional minmax (regret) approach with some of its recent extensions, and several two-stage concepts. A special attention is paid to the computational properties of the robust problems considered.

Suggested Citation

  • Adam Kasperski & Paweł Zieliński, 2016. "Robust Discrete Optimization Under Discrete and Interval Uncertainty: A Survey," 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 113-143, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-33121-8_6
    DOI: 10.1007/978-3-319-33121-8_6
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    Citations

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    Cited by:

    1. Amadeu A. Coco & Andréa Cynthia Santos & Thiago F. Noronha, 2022. "Robust min-max regret covering problems," Computational Optimization and Applications, Springer, vol. 83(1), pages 111-141, September.
    2. Goerigk, Marc & Lendl, Stefan & Wulf, Lasse, 2022. "Recoverable robust representatives selection problems with discrete budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 303(2), pages 567-580.
    3. Marc Goerigk & Adam Kasperski & Paweł Zieliński, 2021. "Combinatorial two-stage minmax regret problems under interval uncertainty," Annals of Operations Research, Springer, vol. 300(1), pages 23-50, May.
    4. Alejandro Crema, 2020. "Min max min robust (relative) regret combinatorial optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 249-283, October.
    5. Büsing, Christina & Comis, Martin & Schmidt, Eva & Streicher, Manuel, 2021. "Robust strategic planning for mobile medical units with steerable and unsteerable demands," European Journal of Operational Research, Elsevier, vol. 295(1), pages 34-50.
    6. Goerigk, Marc & Lendl, Stefan & Wulf, Lasse, 2022. "Two-Stage robust optimization problems with two-stage uncertainty," European Journal of Operational Research, Elsevier, vol. 302(1), pages 62-78.
    7. Goerigk, Marc & Khosravi, Mohammad, 2023. "Optimal scenario reduction for one- and two-stage robust optimization with discrete uncertainty in the objective," European Journal of Operational Research, Elsevier, vol. 310(2), pages 529-551.
    8. Ana Klobučar & Robert Manger, 2020. "Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees," Mathematics, MDPI, vol. 8(2), pages 1-16, February.

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