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The multiple steiner TSP with cyclic order on terminals: valid inequalities and polyhedra

Author

Listed:
  • A. Ridha Mahjoub

    (Kuwait University
    Université Paris-Dauphine PSL)

  • Raouia Taktak

    (ISIMS, Université de Sfax
    Sm@rts, Centre de Recherche en Numérique de Sfax)

  • Eduardo Uchoa

    (Universidade Federal Fluminense)

Abstract

This paper deals with a variant of the Traveling Salesman Problem (TSP), called the Multiple Steiner TSP with Order Constraints (MSTSPOC). Consider an undirected graph with nonnegative weights on the edges, and a set of salesmen such that with each salesman is associated a set of ordered terminals. The MSTSPOC consists in finding a minimum-weight subgraph containing for each salesman a tour going in order through its terminals. We study the polytope associated with the Integer Linear Programming (ILP) formulation proposed in Borne et al. (2013). We characterize when the basic inequalities define facets. We also describe new valid inequalities along with necessary conditions and sufficient conditions for these inequalities to be facet-defining. Further families of valid inequalities, coming from closely related problems, are also discussed. The theoretical results presented in this paper are computationally tested in a companion paper (Taktak 2024).

Suggested Citation

  • A. Ridha Mahjoub & Raouia Taktak & Eduardo Uchoa, 2025. "The multiple steiner TSP with cyclic order on terminals: valid inequalities and polyhedra," Journal of Combinatorial Optimization, Springer, vol. 49(5), pages 1-51, July.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:5:d:10.1007_s10878-025-01288-1
    DOI: 10.1007/s10878-025-01288-1
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    References listed on IDEAS

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    1. Henan Liu & Huili Zhang & Yi Xu, 2021. "The m-Steiner Traveling Salesman Problem with online edge blockages," Journal of Combinatorial Optimization, Springer, vol. 41(4), pages 844-860, May.
    2. 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.
    3. Bektas, Tolga, 2006. "The multiple traveling salesman problem: an overview of formulations and solution procedures," Omega, Elsevier, vol. 34(3), pages 209-219, June.
    4. Xianghu Meng & Jun Li & MengChu Zhou & Shi Cheng, 2021. "A Colored Traveling Salesman Problem with Varying City Colors," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-14, December.
    5. Letchford, Adam N. & Nasiri, Saeideh D. & Theis, Dirk Oliver, 2013. "Compact formulations of the Steiner Traveling Salesman Problem and related problems," European Journal of Operational Research, Elsevier, vol. 228(1), pages 83-92.
    6. Mourad Baïou & Francisco Barahona & Ali Ridha Mahjoub, 2000. "Separation of Partition Inequalities," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 243-254, May.
    7. Éric Duchenne & Gilbert Laporte & Frédéric Semet, 2007. "The Undirected m -Peripatetic Salesman Problem: Polyhedral Results and New Algorithms," Operations Research, INFORMS, vol. 55(5), pages 949-965, October.
    8. José Alejandro Cornejo-Acosta & Jesús García-Díaz & Julio César Pérez-Sansalvador & Carlos Segura, 2023. "Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems," Mathematics, MDPI, vol. 11(13), pages 1-25, July.
    9. Duchenne, Éric & Laporte, Gilbert & Semet, Frédéric, 2012. "The undirected m-Capacitated Peripatetic Salesman Problem," European Journal of Operational Research, Elsevier, vol. 223(3), pages 637-643.
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