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An exact algorithm and a metaheuristic for the multi-vehicle covering tour problem with a constraint on the number of vertices

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  • Hà, Minh Hoàng
  • Bostel, Nathalie
  • Langevin, André
  • Rousseau, Louis-Martin

Abstract

The multi-vehicle covering tour problem (m-CTP) involves finding a minimum-length set of vehicle routes passing through a subset of vertices, subject to constraints on the length of each route and the number of vertices that it contains, such that each vertex not included in any route lies within a given distance of a route. This paper tackles a particular case of m-CTP where only the restriction on the number of vertices is considered, i.e., the constraint on the length is relaxed. The problem is solved by a branch-and-cut algorithm and a metaheuristic. To develop the branch-and-cut algorithm, we use a new integer programming formulation based on a two-commodity flow model. The metaheuristic is based on the evolutionary local search (ELS) method proposed in [23]. Computational results are reported for a set of test problems derived from the TSPLIB.

Suggested Citation

  • Hà, Minh Hoàng & Bostel, Nathalie & Langevin, André & Rousseau, Louis-Martin, 2013. "An exact algorithm and a metaheuristic for the multi-vehicle covering tour problem with a constraint on the number of vertices," European Journal of Operational Research, Elsevier, vol. 226(2), pages 211-220.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:2:p:211-220
    DOI: 10.1016/j.ejor.2012.11.012
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    References listed on IDEAS

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    Cited by:

    1. Allahyari, Somayeh & Salari, Majid & Vigo, Daniele, 2015. "A hybrid metaheuristic algorithm for the multi-depot covering tour vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 242(3), pages 756-768.
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    5. David A. Flores-Garza & M. Angélica Salazar-Aguilar & Sandra Ulrich Ngueveu & Gilbert Laporte, 2017. "The multi-vehicle cumulative covering tour problem," Annals of Operations Research, Springer, vol. 258(2), pages 761-780, November.
    6. Veenstra, Marjolein & Roodbergen, Kees Jan & Coelho, Leandro C. & Zhu, Stuart X., 2018. "A simultaneous facility location and vehicle routing problem arising in health care logistics in the Netherlands," European Journal of Operational Research, Elsevier, vol. 268(2), pages 703-715.
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    8. Zhou, Lin & Baldacci, Roberto & Vigo, Daniele & Wang, Xu, 2018. "A Multi-Depot Two-Echelon Vehicle Routing Problem with Delivery Options Arising in the Last Mile Distribution," European Journal of Operational Research, Elsevier, vol. 265(2), pages 765-778.
    9. Christian Artigues & Nicolas Jozefowiez & Boadu M. Sarpong, 2018. "Column generation algorithms for bi-objective combinatorial optimization problems with a min–max objective," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 117-142, June.
    10. Salman, F. Sibel & Yücel, Eda & Kayı, İlker & Turper-Alışık, Sedef & Coşkun, Abdullah, 2021. "Modeling mobile health service delivery to Syrian migrant farm workers using call record data," Socio-Economic Planning Sciences, Elsevier, vol. 77(C).
    11. Karaoğlan, İsmail & Erdoğan, Güneş & Koç, Çağrı, 2018. "The Multi-Vehicle Probabilistic Covering Tour Problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 278-287.
    12. Glize, Estèle & Roberti, Roberto & Jozefowiez, Nicolas & Ngueveu, Sandra Ulrich, 2020. "Exact methods for mono-objective and Bi-Objective Multi-Vehicle Covering Tour Problems," European Journal of Operational Research, Elsevier, vol. 283(3), pages 812-824.
    13. Eda Yücel & F. Sibel Salman & Burçin Bozkaya & Cemre Gökalp, 2020. "A data-driven optimization framework for routing mobile medical facilities," Annals of Operations Research, Springer, vol. 291(1), pages 1077-1102, August.
    14. Raghavan, S. & Sahin, Mustafa & Salman, F. Sibel, 2019. "The capacitated mobile facility location problem," European Journal of Operational Research, Elsevier, vol. 277(2), pages 507-520.
    15. Bulhões, Teobaldo & Hà, Minh Hoàng & Martinelli, Rafael & Vidal, Thibaut, 2018. "The vehicle routing problem with service level constraints," European Journal of Operational Research, Elsevier, vol. 265(2), pages 544-558.
    16. Roberto Baldacci & Sandra Ulrich Ngueveu & Roberto Wolfler Calvo, 2017. "The Vehicle Routing Problem with Transhipment Facilities," Transportation Science, INFORMS, vol. 51(2), pages 592-606, May.

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