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A new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem

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  • Chassein, André B.
  • Goerigk, Marc

Abstract

Minmax regret optimization aims at finding robust solutions that perform best in the worst-case, compared to the respective optimum objective value in each scenario. Even for simple uncertainty sets like boxes, most polynomially solvable optimization problems have strongly NP-complete minmax regret counterparts. Thus, heuristics with performance guarantees can potentially be of great value, but only few such guarantees exist.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:3:p:739-747
    DOI: 10.1016/j.ejor.2015.02.023
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    References listed on IDEAS

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    1. Averbakh, Igor & Lebedev, Vasilij, 2005. "On the complexity of minmax regret linear programming," European Journal of Operational Research, Elsevier, vol. 160(1), pages 227-231, January.
    2. Conde, Eduardo, 2012. "On a constant factor approximation for minmax regret problems using a symmetry point scenario," European Journal of Operational Research, Elsevier, vol. 219(2), pages 452-457.
    3. James Roskind & Robert E. Tarjan, 1985. "A Note on Finding Minimum-Cost Edge-Disjoint Spanning Trees," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 701-708, November.
    4. Montemanni, Roberto, 2006. "A Benders decomposition approach for the robust spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1479-1490, November.
    5. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2007. "Approximation of min-max and min-max regret versions of some combinatorial optimization problems," European Journal of Operational Research, Elsevier, vol. 179(2), pages 281-290, June.
    6. 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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    Citations

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    Cited by:

    1. Chassein, André & Dokka, Trivikram & Goerigk, Marc, 2019. "Algorithms and uncertainty sets for data-driven robust shortest path problems," European Journal of Operational Research, Elsevier, vol. 274(2), pages 671-686.
    2. 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.
    3. Chassein, André & Goerigk, Marc, 2017. "Minmax regret combinatorial optimization problems with ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 258(1), pages 58-69.
    4. 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.
    5. Lee, Jisun & Joung, Seulgi & Lee, Kyungsik, 2022. "A fully polynomial time approximation scheme for the probability maximizing shortest path problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 35-45.
    6. Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    7. Buu-Chau Truong & Kim-Hung Pho & Van-Buol Nguyen & Bui Anh Tuan & Wing-Keung Wong, 2019. "Graph Theory And Environmental Algorithmic Solutions To Assign Vehicles Application To Garbage Collection In Vietnam," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(3), pages 1-35, September.

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