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Decremental State-Space Relaxations for the Basic Traveling Salesman Problem with a Drone

Author

Listed:
  • Marcos Blufstein

    (Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina)

  • Gonzalo Lera-Romero

    (Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina)

  • Francisco J. Soulignac

    (Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina; Instituto de Investigación en Ciencias de la Computación (ICC), CONICET-Universidad de Buenos Aires, Buenos Aires C1428EGA, Argentina)

Abstract

Truck-and-drone routing problems have become an important research topic in the last decade because of their applications for last-mile deliveries. Despite the many publications in this area, the most efficient exact algorithms designed thus far struggle to solve the benchmark instances with 39 or more customers. This fact holds even for one of the simplest variants involving one truck and one drone whose routes must synchronize at customers’ locations: the basic traveling salesman problem with a drone (TSP-D). In this article, we devise a new algorithm for the TSP-D that solves every benchmark instance with up to 59 customers, and it scales up to 99 customers when the drone is much faster than the truck. The core of our method is a dynamic programming algorithm that is applied for column generation and variable fixing within tailored decremental state-space relaxation strategies.

Suggested Citation

  • Marcos Blufstein & Gonzalo Lera-Romero & Francisco J. Soulignac, 2024. "Decremental State-Space Relaxations for the Basic Traveling Salesman Problem with a Drone," INFORMS Journal on Computing, INFORMS, vol. 36(4), pages 1064-1083, July.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:4:p:1064-1083
    DOI: 10.1287/ijoc.2022.0390
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    References listed on IDEAS

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    1. Stefan Poikonen & Bruce Golden & Edward A. Wasil, 2019. "A Branch-and-Bound Approach to the Traveling Salesman Problem with a Drone," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 335-346, April.
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    4. Gonzalo Lera-Romero & Juan José Miranda Bront & Francisco J. Soulignac, 2022. "Dynamic Programming for the Time-Dependent Traveling Salesman Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3292-3308, November.
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