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A branch-and-cut algorithm for the generalized traveling salesman problem with time windows

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  • Yuan, Yuan
  • Cattaruzza, Diego
  • Ogier, Maxime
  • Semet, Frédéric

Abstract

The generalized traveling salesman problem with time windows (GTSPTW) is defined on a directed graph where the vertex set is partitioned into clusters. One cluster contains only the depot. Each vertex is associated with a time interval, the time window, during which the visit must take place if the vertex is visited. The objective is to find a minimum cost tour starting and ending at the depot such that each cluster is visited exactly once and time constraints are respected, i.e., for each cluster, one vertex is visited during its time window. In this paper, two integer linear programming formulations for GTSPTW are provided as well as several problem-specific valid inequalities. A branch-and-cut algorithm is developed in which the inequalities are separated dynamically. To reduce the computation times, an initial upper bound is provided by a simple and fast heuristic. We propose different sets of instances characterized by their time window structures. Experimental results show that our algorithm is effective and instances including up to 30 clusters can be solved to optimality within one hour.

Suggested Citation

  • Yuan, Yuan & Cattaruzza, Diego & Ogier, Maxime & Semet, Frédéric, 2020. "A branch-and-cut algorithm for the generalized traveling salesman problem with time windows," European Journal of Operational Research, Elsevier, vol. 286(3), pages 849-866.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:3:p:849-866
    DOI: 10.1016/j.ejor.2020.04.024
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    3. Zang, Xiaoning & Jiang, Li & Liang, Changyong & Fang, Xiang, 2023. "Coordinated home and locker deliveries: An exact approach for the urban delivery problem with conflicting time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    4. Khachai, Daniil & Sadykov, Ruslan & Battaia, Olga & Khachay, Michael, 2023. "Precedence constrained generalized traveling salesman problem: Polyhedral study, formulations, and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 309(2), pages 488-505.
    5. Yuan, Yuan & Cattaruzza, Diego & Ogier, Maxime & Semet, Frédéric & Vigo, Daniele, 2021. "A column generation based heuristic for the generalized vehicle routing problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).

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