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An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows

Author

Listed:
  • Gilles Pesant

    (Centre de recherche sur les transports, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal H3C 3J7, Canada)

  • Michel Gendreau

    (Centre de recherche sur les transports and Département d'informatique et de recherche opérationnelle, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal H3C 3J7, Canada)

  • Jean-Yves Potvin

    (Centre de recherche sur les transports and Département d'informatique et de recherche opérationnelle, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal H3C 3J7, Canada)

  • Jean-Marc Rousseau

    (Centre de recherche sur les transports and Département d'informatique et de recherche opérationnelle, Université de Montréal, C.P. 6128, succursale Centre-ville, Montréal H3C 3J7, and GIRO, Inc., 75 rue de Port-Royal est, bureau #500, Montréal H3L 3T1, Canada)

Abstract

This paper presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branch-and-bound optimization algorithm without any restrictive assumption on the time windows. Unlike dynamic programming approaches whose performance relies heavily on the degree of discretization applied to the data, our algorithm does not suffer from such space-complexity issues. The data-driven mechanism at its core more fully exploits pruning rules developed in operations research by using them not only a priori but also dynamically during the search. Computational results are reported and comparisons are made with both exact and heuristic algorithms. On Solomon's well-known test bed, our algorithm is instrumental in achieving new best solutions for some of the problems in set RC2 and strengthens the presumption of optimality for the best known solutions to the problems in set C2.

Suggested Citation

  • Gilles Pesant & Michel Gendreau & Jean-Yves Potvin & Jean-Marc Rousseau, 1998. "An Exact Constraint Logic Programming Algorithm for the Traveling Salesman Problem with Time Windows," Transportation Science, INFORMS, vol. 32(1), pages 12-29, February.
    • Handle: RePEc:inm:ortrsc:v:32:y:1998:i:1:p:12-29
    DOI: 10.1287/trsc.32.1.12
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    References listed on IDEAS

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    1. Yvan Dumas & Jacques Desrosiers & Eric Gelinas & Marius M. Solomon, 1995. "An Optimal Algorithm for the Traveling Salesman Problem with Time Windows," Operations Research, INFORMS, vol. 43(2), pages 367-371, April.
    2. Martin W. P. Savelsbergh, 1992. "The Vehicle Routing Problem with Time Windows: Minimizing Route Duration," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 146-154, May.
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    Cited by:

    1. Filippo Focacci & Andrea Lodi & Michela Milano, 2002. "A Hybrid Exact Algorithm for the TSPTW," INFORMS Journal on Computing, INFORMS, vol. 14(4), pages 403-417, November.
    2. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2012. "New State-Space Relaxations for Solving the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 356-371, August.
    3. Dieter, Peter & Caron, Matthew & Schryen, Guido, 2023. "Integrating driver behavior into last-mile delivery routing: Combining machine learning and optimization in a hybrid decision support framework," European Journal of Operational Research, Elsevier, vol. 311(1), pages 283-300.
    4. Olli Bräysy & Michel Gendreau, 2005. "Vehicle Routing Problem with Time Windows, Part II: Metaheuristics," Transportation Science, INFORMS, vol. 39(1), pages 119-139, February.
    5. Russell, Robert, 2013. "A constraint programming approach to designing a newspaper distribution system," International Journal of Production Economics, Elsevier, vol. 145(1), pages 132-138.
    6. Andrea Lodi & Michela Milano & Louis-Martin Rousseau, 2006. "Discrepancy-Based Additive Bounding Procedures," INFORMS Journal on Computing, INFORMS, vol. 18(4), pages 480-493, November.
    7. Ann M. Campbell & Barrett W. Thomas, 2008. "Probabilistic Traveling Salesman Problem with Deadlines," Transportation Science, INFORMS, vol. 42(1), pages 1-21, February.
    8. Sanjeeb Dash & Oktay Günlük & Andrea Lodi & Andrea Tramontani, 2012. "A Time Bucket Formulation for the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 132-147, February.
    9. Jeffrey W. Ohlmann & Barrett W. Thomas, 2007. "A Compressed-Annealing Heuristic for the Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 80-90, February.
    10. Majed G. Alharbi & Ahmed Stohy & Mohammed Elhenawy & Mahmoud Masoud & Hamiden Abd El-Wahed Khalifa, 2021. "Solving Traveling Salesman Problem with Time Windows Using Hybrid Pointer Networks with Time Features," Sustainability, MDPI, vol. 13(22), pages 1-12, November.
    11. Natashia L. Boland & Martin W. P. Savelsbergh, 2019. "Perspectives on integer programming for time-dependent models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 147-173, July.
    12. Gerardo Berbeglia & Gilles Pesant & Louis-Martin Rousseau, 2011. "Checking the Feasibility of Dial-a-Ride Instances Using Constraint Programming," Transportation Science, INFORMS, vol. 45(3), pages 399-412, August.
    13. Pesant, Gilles & Gendreau, Michel & Potvin, Jean-Yves & Rousseau, Jean-Marc, 1999. "On the flexibility of constraint programming models: From single to multiple time windows for the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 117(2), pages 253-263, September.
    14. Mor, A. & Speranza, M.G. & Viegas, J.M., 2020. "Efficient loading and unloading operations via a booking system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    15. Anirudh Subramanyam & Chrysanthos E. Gounaris, 2018. "A Decomposition Algorithm for the Consistent Traveling Salesman Problem with Vehicle Idling," Transportation Science, INFORMS, vol. 52(2), pages 386-401, March.
    16. Fontaine, Romain & Dibangoye, Jilles & Solnon, Christine, 2023. "Exact and anytime approach for solving the time dependent traveling salesman problem with time windows," European Journal of Operational Research, Elsevier, vol. 311(3), pages 833-844.
    17. Albiach, José & Sanchis, José Marí­a & Soler, David, 2008. "An asymmetric TSP with time windows and with time-dependent travel times and costs: An exact solution through a graph transformation," European Journal of Operational Research, Elsevier, vol. 189(3), pages 789-802, September.
    18. Tarhan, İstenç & Oğuz, Ceyda, 2022. "A matheuristic for the generalized order acceptance and scheduling problem," European Journal of Operational Research, Elsevier, vol. 299(1), pages 87-103.
    19. John S. F. Lyons & Peter C. Bell & Mehmet A. Begen, 2018. "Solving the Whistler-Blackcomb Mega Day Challenge," Interfaces, INFORMS, vol. 48(4), pages 323-339, August.

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