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Analysis and Branch-and-Cut Algorithm for the Time-Dependent Travelling Salesman Problem

Author

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  • Jean-François Cordeau

    (CIRRELT, HEC Montréal, Montréal H3T 2A7, Canada)

  • Gianpaolo Ghiani

    (Dipartimento di Ingegneria dell'Innovazione, Università del Salento, 73100 Lecce, Italy)

  • Emanuela Guerriero

    (Dipartimento di Ingegneria dell'Innovazione, Università del Salento, 73100 Lecce, Italy)

Abstract

Given a graph whose arc traversal times vary over time, the time-dependent travelling salesman problem (TDTSP) consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The contribution of this paper is twofold. First, we describe a lower and upper bounding procedure that requires the solution of a simpler (yet NP-hard) asymmetric travelling salesman problem (ATSP). In addition, we prove that this ATSP solution is optimal for the TDTSP if all the arcs share a common congestion pattern. Second, we formulate the TDTSP as an integer linear programming model for which valid inequalities are devised. These inequalities are then embedded into a branch-and-cut algorithm that is able to solve instances with up to 40 vertices.

Suggested Citation

  • Jean-François Cordeau & Gianpaolo Ghiani & Emanuela Guerriero, 2014. "Analysis and Branch-and-Cut Algorithm for the Time-Dependent Travelling Salesman Problem," Transportation Science, INFORMS, vol. 48(1), pages 46-58, February.
    • Handle: RePEc:inm:ortrsc:v:48:y:2014:i:1:p:46-58
    DOI: 10.1287/trsc.1120.0449
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    References listed on IDEAS

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    1. Gouveia, Luis & Vo[ss], Stefan, 1995. "A classification of formulations for the (time-dependent) traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 69-82, May.
    2. Malandraki, Chryssi & Dial, Robert B., 1996. "A restricted dynamic programming heuristic algorithm for the time dependent traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 90(1), pages 45-55, April.
    3. Ahuja, Ravindra & Orlin, James & Pallottino, Stefano & Scutella, Maria, 2003. "Dynamic Shortest Paths Minimizing Travel Times And Costs," Working papers 4390-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. 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.
    5. Chryssi Malandraki & Mark S. Daskin, 1992. "Time Dependent Vehicle Routing Problems: Formulations, Properties and Heuristic Algorithms," Transportation Science, INFORMS, vol. 26(3), pages 185-200, August.
    6. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    7. 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.
    8. Schneider, Johannes, 2002. "The time-dependent traveling salesman problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 151-155.
    9. Donati, Alberto V. & Montemanni, Roberto & Casagrande, Norman & Rizzoli, Andrea E. & Gambardella, Luca M., 2008. "Time dependent vehicle routing problem with a multi ant colony system," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1174-1191, March.
    10. Jean-Claude Picard & Maurice Queyranne, 1978. "The Time-Dependent Traveling Salesman Problem and Its Application to the Tardiness Problem in One-Machine Scheduling," Operations Research, INFORMS, vol. 26(1), pages 86-110, February.
    11. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, January.
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    2. He, Xuan & Pan, Quan-Ke & Gao, Liang & Neufeld, Janis S., 2023. "An asymmetric traveling salesman problem based matheuristic algorithm for flowshop group scheduling problem," European Journal of Operational Research, Elsevier, vol. 310(2), pages 597-610.
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    5. 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.
    6. Taş, Duygu & Gendreau, Michel & Jabali, Ola & Laporte, Gilbert, 2016. "The traveling salesman problem with time-dependent service times," European Journal of Operational Research, Elsevier, vol. 248(2), pages 372-383.
    7. Lera-Romero, Gonzalo & Miranda Bront, Juan José & Soulignac, Francisco J., 2024. "A branch-cut-and-price algorithm for the time-dependent electric vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 312(3), pages 978-995.
    8. Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.
    9. Sun, Peng & Veelenturf, Lucas P. & Hewitt, Mike & Van Woensel, Tom, 2020. "Adaptive large neighborhood search for the time-dependent profitable pickup and delivery problem with time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 138(C).
    10. Rifki, Omar & Chiabaut, Nicolas & Solnon, Christine, 2020. "On the impact of spatio-temporal granularity of traffic conditions on the quality of pickup and delivery optimal tours," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    11. Adamo, Tommaso & Gendreau, Michel & Ghiani, Gianpaolo & Guerriero, Emanuela, 2024. "A review of recent advances in time-dependent vehicle routing," European Journal of Operational Research, Elsevier, vol. 319(1), pages 1-15.
    12. Gianpaolo Ghiani & Emanuela Guerriero, 2014. "A Note on the Ichoua, Gendreau, and Potvin (2003) Travel Time Model," Transportation Science, INFORMS, vol. 48(3), pages 458-462, August.
    13. Vu, Duc Minh & Hewitt, Mike & Vu, Duc D., 2022. "Solving the time dependent minimum tour duration and delivery man problems with dynamic discretization discovery," European Journal of Operational Research, Elsevier, vol. 302(3), pages 831-846.
    14. Remy Spliet & Said Dabia & Tom Van Woensel, 2018. "The Time Window Assignment Vehicle Routing Problem with Time-Dependent Travel Times," Transportation Science, INFORMS, vol. 52(2), pages 261-276, March.
    15. Jianbin Xin & Benyang Yu & Andrea D’Ariano & Heshan Wang & Meng Wang, 2022. "Time-dependent rural postman problem: time-space network formulation and genetic algorithm," Operational Research, Springer, vol. 22(3), pages 2943-2972, July.
    16. Pottel, Steffen & Goel, Asvin, 2022. "Scheduling activities with time-dependent durations and resource consumptions," European Journal of Operational Research, Elsevier, vol. 301(2), pages 445-457.
    17. Hailong Huang & Andrey V. Savkin, 2020. "Energy-Efficient Autonomous Navigation of Solar-Powered UAVs for Surveillance of Mobile Ground Targets in Urban Environments," Energies, MDPI, vol. 13(21), pages 1-17, October.

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