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The Robust Traveling Salesman Problem with Interval Data

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  • R. Montemanni

    (Istituto Dalle Molle di Studi sull’Intelligenza Artificiale, Galleria 2, CH-6928 Lugano-Manno, Switzerland)

  • J. Barta

    (Istituto Dalle Molle di Studi sull’Intelligenza Artificiale, Galleria 2, CH-6928 Lugano-Manno, Switzerland)

  • M. Mastrolilli

    (Istituto Dalle Molle di Studi sull’Intelligenza Artificiale, Galleria 2, CH-6928 Lugano-Manno, Switzerland)

  • L. M. Gambardella

    (Istituto Dalle Molle di Studi sull’Intelligenza Artificiale, Galleria 2, CH-6928 Lugano-Manno, Switzerland)

Abstract

The traveling salesman problem is one of the most famous combinatorial optimization problems and has been intensively studied. Many extensions to the basic problem have also been proposed, with the aim of making the resulting mathematical models as realistic as possible. We present a new extension to the basic problem, where travel times are specified as a range of possible values. This model reflects the intrinsic difficulties of estimating travel times in reality. We apply the robust deviation criterion to drive optimization over the interval data problem so obtained. Some interesting theoretical properties of the new optimization problems are identified and discussed, together with a new mathematical formulation and some exact and heuristic algorithms. Computational experiments are finally presented.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:41:y:2007:i:3:p:366-381
    DOI: 10.1287/trsc.1060.0181
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    References listed on IDEAS

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    12. Groß, Patrick-Oliver & Ehmke, Jan Fabian & Mattfeld, Dirk Christian, 2020. "Interval travel times for robust synchronization in city logistics vehicle routing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
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    14. 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.
    15. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    16. 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.
    17. Yin, Yunqiang & Luo, Zunhao & Wang, Dujuan & Cheng, T.C.E., 2023. "Wasserstein distance‐based distributionally robust parallel‐machine scheduling," Omega, Elsevier, vol. 120(C).
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