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Heuristic solutions to robust variants of the minimum-cost integer flow problem

Author

Listed:
  • Marko Špoljarec

    (Privredna banka Zagreb)

  • Robert Manger

    (University of Zagreb)

Abstract

This paper deals with robust optimization applied to network flows. We consider two robust variants of the minimum-cost integer flow problem. Thereby, uncertainty in problem formulation is limited to arc costs and expressed by a finite set of explicitly given scenarios. It turns out that both problem variants are NP-hard. To solve the considered variants, we propose several heuristics based on local search or evolutionary computing. We also evaluate our heuristics experimentally on appropriate problem instances.

Suggested Citation

  • Marko Špoljarec & Robert Manger, 2020. "Heuristic solutions to robust variants of the minimum-cost integer flow problem," Journal of Heuristics, Springer, vol. 26(4), pages 531-559, August.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:4:d:10.1007_s10732-020-09441-1
    DOI: 10.1007/s10732-020-09441-1
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    References listed on IDEAS

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    1. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    2. Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
    3. Dimitris Bertsimas & Ebrahim Nasrabadi & Sebastian Stiller, 2013. "Robust and Adaptive Network Flows," Operations Research, INFORMS, vol. 61(5), pages 1218-1242, October.
    4. Roy, Bernard, 2010. "Robustness in operational research and decision aiding: A multi-faceted issue," European Journal of Operational Research, Elsevier, vol. 200(3), pages 629-638, February.
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