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An Iterated Dual Substitution Approach for Binary Integer Programming Problems Under the Min-Max Regret Criterion

Author

Listed:
  • Wei Wu

    (Department of Engineering, Shizuoka University, Hamamatsu 432-8561, Japan)

  • Manuel Iori

    (Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy)

  • Silvano Martello

    (DEI “Guglielmo Marconi”, Alma Mater Studiorum University of Bologna, 40126 Bologna, Italy)

  • Mutsunori Yagiura

    (Department of Mathematical Informatics, Nagoya University, Nagoya 464-8601, Japan)

Abstract

We consider binary integer programming problems with the min-max regret objective function under interval objective coefficients. We propose a heuristic framework, the iterated dual substitution (iDS) algorithm, which iteratively invokes a dual substitution heuristic and excludes from the search space any solution already checked in previous iterations. In iDS, we use a best scenario–based lemma to improve performance. We apply iDS to four typical combinatorial optimization problems: the knapsack problem, the multidimensional knapsack problem, the generalized assignment problem, and the set covering problem. For the multidimensional knapsack problem, we compare the iDS approach with two algorithms widely used for problems with the min-max regret criterion: a fixed-scenario approach, and a branch-and-cut approach. The results of computational experiments on a broad set of benchmark instances show that the proposed iDS approach performs best on most tested instances. For the knapsack problem, the generalized assignment problem, and the set covering problem, we compare iDS with state-of-the-art results. The iDS algorithm successfully updates best-known records for a number of benchmark instances. Summary of Contribution: This paper proposes a heuristic framework for binary integer programming (BIP) problems with the min-max regret objective function under interval objective coefficients. We selected four representative NP-hard combinatorial optimization problems: the knapsack problem, the multidimensional knapsack problem, the set covering problem, and the generalized assignment problem. We show the effectiveness and efficiency of the approach by comparing with state-of-the-art results.

Suggested Citation

  • Wei Wu & Manuel Iori & Silvano Martello & Mutsunori Yagiura, 2022. "An Iterated Dual Substitution Approach for Binary Integer Programming Problems Under the Min-Max Regret Criterion," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2523-2539, September.
  • Handle: RePEc:inm:orijoc:v:34:y:2022:i:5:p:2523-2539
    DOI: 10.1287/ijoc.2022.1189
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    References listed on IDEAS

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    1. Dong, C. & Huang, G.H. & Cai, Y.P. & Xu, Y., 2011. "An interval-parameter minimax regret programming approach for power management systems planning under uncertainty," Applied Energy, Elsevier, vol. 88(8), pages 2835-2845, August.
    2. Laguna, Manuel & Kelly, James P. & Gonzalez-Velarde, JoseLuis & Glover, Fred, 1995. "Tabu search for the multilevel generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 82(1), pages 176-189, April.
    3. Montemanni, R. & Gambardella, L. M., 2005. "A branch and bound algorithm for the robust spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 161(3), pages 771-779, March.
    4. Jakob Puchinger & Günther R. Raidl & Ulrich Pferschy, 2010. "The Multidimensional Knapsack Problem: Structure and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 250-265, May.
    5. Ayvaz-Cavdaroglu, Nur & Kachani, Soulaymane & Maglaras, Costis, 2016. "Revenue management with minimax regret negotiations," Omega, Elsevier, vol. 63(C), pages 12-22.
    6. 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.
    7. Hamed Poorsepahy-Samian & Reza Kerachian & Mohammad Nikoo, 2012. "Water and Pollution Discharge Permit Allocation to Agricultural Zones: Application of Game Theory and Min-Max Regret Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4241-4257, November.
    8. Fabio Furini & Manuel Iori & Silvano Martello & Mutsunori Yagiura, 2015. "Heuristic and Exact Algorithms for the Interval Min–Max Regret Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 392-405, May.
    9. 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.
    10. R. Montemanni & J. Barta & M. Mastrolilli & L. M. Gambardella, 2007. "The Robust Traveling Salesman Problem with Interval Data," Transportation Science, INFORMS, vol. 41(3), pages 366-381, August.
    11. Xidonas, Panos & Mavrotas, George & Hassapis, Christis & Zopounidis, Constantin, 2017. "Robust multiobjective portfolio optimization: A minimax regret approach," European Journal of Operational Research, Elsevier, vol. 262(1), pages 299-305.
    12. Jordi Pereira & Igor Averbakh, 2013. "The Robust Set Covering Problem with interval data," Annals of Operations Research, Springer, vol. 207(1), pages 217-235, August.
    13. Mariusz Makuchowski, 2014. "Perturbation algorithm for a minimax regret minimum spanning tree problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(1), pages 37-49.
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    Cited by:

    1. Ling, Chunyan & Yang, Lechang & Feng, Kaixuan & Kuo, Way, 2023. "Survival signature based robust redundancy allocation under imprecise probability," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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