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Robust combinatorial optimization problems under budgeted interdiction uncertainty

Author

Listed:
  • Marc Goerigk

    (University of Passau)

  • Mohammad Khosravi

    (University of Passau)

Abstract

In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the complexity of the corresponding robust problem. For this reason, budgeted uncertainty sets are often studied, as they enable us to decompose the robust problem into easier subproblems. We propose a variant of discrete budgeted uncertainty for cardinality-based constraints or objectives, where a weight vector is applied to the budget constraint. We show that while the adversarial problem can be solved in linear time, the robust problem becomes NP-hard and not approximable. We discuss different possibilities to model the robust problem and show experimentally that despite the hardness result, some models scale relatively well in the problem size.

Suggested Citation

  • Marc Goerigk & Mohammad Khosravi, 2025. "Robust combinatorial optimization problems under budgeted interdiction uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 47(1), pages 255-285, March.
    • Handle: RePEc:spr:orspec:v:47:y:2025:i:1:d:10.1007_s00291-024-00772-0
    DOI: 10.1007/s00291-024-00772-0
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    References listed on IDEAS

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    1. Christoph Buchheim & Jannis Kurtz, 2018. "Robust combinatorial optimization under convex and discrete cost uncertainty," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 211-238, September.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. Marc Goerigk & Adam Kasperski & Paweł Zieliński, 2022. "Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 497-527, April.
    4. Bohle, Carlos & Maturana, Sergio & Vera, Jorge, 2010. "A robust optimization approach to wine grape harvesting scheduling," European Journal of Operational Research, Elsevier, vol. 200(1), pages 245-252, January.
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