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The Multiple Steiner TSP with order constraints: complexity and optimization algorithms

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Abstract

We consider a variant of the Travelling Salesman Problem (TSP), the Multiple Steiner TSP with Order constraints (MSTSPO). Consider a weighted undirected graph and a set of salesmen, and each salesman is associated with a set of compulsory vertices to visit, called terminals. The MSTSPO consists in finding a minimum-cost subgraph containing for each salesman a tour going in a specified order through its terminals. Along with its importance from a theoretical point of view, the problem is also challenging in practice since it has applications in telecommunication networks. We show that the problem is NP-hard even for a single salesman and propose integer programming formulations. We then devise both Branch-and-Cut and Branch-and-Price algorithms to solve the problem. The extensive computational results are presented, showing the efficiency of our algorithms.

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Acknowledgements

The authors would like to thank Eric Gourdin and Nancy Perrot from Orange Labs, France, and Sylvie Borne from LIPN Univesité Paris 13, France, for their fruitful collaboration.

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Authors and Affiliations

  1. PSL Research University, CNRS, LAMSADE, Université Paris-Dauphine, 75016, Paris, France

    Virginie Gabrel & A. Ridha Mahjoub

  2. ISIMS and LT2S/CRNS, Université de Sfax, Sfax, Tunisia

    Raouia Taktak

  3. Departamento de Engenharia de Produção, Universidade Federal Fluminense, Niterói, RJ, Brasil

    Eduardo Uchoa

Authors
  1. Virginie Gabrel
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  2. A. Ridha Mahjoub
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  3. Raouia Taktak
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  4. Eduardo Uchoa
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Corresponding author

Correspondence to Raouia Taktak.

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Gabrel, V., Mahjoub, A.R., Taktak, R. et al. The Multiple Steiner TSP with order constraints: complexity and optimization algorithms. Soft Comput 24, 17957–17968 (2020). https://doi.org/10.1007/s00500-020-05043-y

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