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POPMUSIC for the travelling salesman problem

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  • Taillard, Éric D.
  • Helsgaun, Keld

Abstract

POPMUSIC— Partial OPtimization Metaheuristic Under Special Intensification Conditions — is a template for tackling large problem instances. This metaheuristic has been shown to be very efficient for various hard combinatorial problems such as p-median, sum of squares clustering, vehicle routing, map labelling and location routing. A key point for treating large Travelling Salesman Problem (TSP) instances is to consider only a subset of edges connecting the cities. The main goal of this article is to present how to build a list of good candidate edges with a complexity lower than quadratic in the context of TSP instances given by a general function. The candidate edges are found with a technique exploiting tour merging and the POPMUSIC metaheuristic. When these candidate edges are provided to a good local search engine, high quality solutions can be found quite efficiently. The method is tested on TSP instances of up to several million cities with different structures (Euclidean uniform, clustered, 2D to 5D, grids, toroidal distances). Numerical results show that solutions of excellent quality can be obtained with an empirical complexity lower than quadratic without exploiting the geometrical properties of the instances.

Suggested Citation

  • Taillard, Éric D. & Helsgaun, Keld, 2019. "POPMUSIC for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 420-429.
    • Handle: RePEc:eee:ejores:v:272:y:2019:i:2:p:420-429
    DOI: 10.1016/j.ejor.2018.06.039
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    References listed on IDEAS

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    1. David Applegate & William Cook & André Rohe, 2003. "Chained Lin-Kernighan for Large Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 82-92, February.
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    2. Emde, Simon & Tahirov, Nail & Gendreau, Michel & Glock, Christoph H., 2021. "Routing automated lane-guided transport vehicles in a warehouse handling returns," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1085-1098.
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    4. Boldizsár Tüű-Szabó & Péter Földesi & László T. Kóczy, 2024. "An Efficient Tour Construction Heuristic for Generating the Candidate Set of the Traveling Salesman Problem with Large Sizes," Mathematics, MDPI, vol. 12(19), pages 1-21, September.
    5. Bock, Stefan & Bomsdorf, Stefan & Boysen, Nils & Schneider, Michael, 2025. "A survey on the Traveling Salesman Problem and its variants in a warehousing context," European Journal of Operational Research, Elsevier, vol. 322(1), pages 1-14.
    6. Abtin Nourmohammadzadeh & Malek Sarhani & Stefan Voß, 2023. "A matheuristic approach for the family traveling salesman problem," Journal of Heuristics, Springer, vol. 29(4), pages 435-460, December.
    7. Dontas, Michael & Sideris, Georgios & Manousakis, Eleftherios G. & Zachariadis, Emmanouil E., 2023. "An adaptive memory matheuristic for the set orienteering problem," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1010-1023.
    8. Alberto Santini & Michael Schneider & Thibaut Vidal & Daniele Vigo, 2023. "Decomposition Strategies for Vehicle Routing Heuristics," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 543-559, May.

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