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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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    7. Avraham, Edison & Raviv, Tal, 2020. "The data-driven time-dependent traveling salesperson problem," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 25-40.
    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. 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.
    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. 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.
    14. 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.
    15. 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.
    16. 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.

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