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A linearithmic heuristic for the travelling salesman problem

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  • Taillard, Éric D.

Abstract

A linearithmic (nlogn) randomized method based on POPMUSIC (Partial Optimization Metaheuristic Under Special Intensification Conditions) is proposed for generating reasonably good solutions to the travelling salesman problem. The method improves a previous work with empirical algorithmic complexity in n1.6. The method has been tested on instances with billions of cities. For a lot of problem instances of the literature, a few dozens of runs are able to generate a very high proportion of the edges of the best solutions known. This characteristic is exploited in a new release of the Helsgaun’s implementation of the Lin-Kernighan heuristic (LKH) that is also able to produce rapidly extremely good solutions for non-Euclidean instances. The practical limits of the proposed method are discussed on a new type of problem instances arising in a manufacturing process, especially in 3D extrusion printing.

Suggested Citation

  • Taillard, Éric D., 2022. "A linearithmic heuristic for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 442-450.
    • Handle: RePEc:eee:ejores:v:297:y:2022:i:2:p:442-450
    DOI: 10.1016/j.ejor.2021.05.034
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    References listed on IDEAS

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    1. Quang Minh Ha & Yves Deville & Quang Dung Pham & Minh Hoàng Hà, 2020. "A hybrid genetic algorithm for the traveling salesman problem with drone," Journal of Heuristics, Springer, vol. 26(2), pages 219-247, April.
    2. 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.
    3. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    4. G Laporte & U Palekar, 2002. "Some applications of the clustered travelling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(9), pages 972-976, September.
    5. Rego, César & Gamboa, Dorabela & Glover, Fred & Osterman, Colin, 2011. "Traveling salesman problem heuristics: Leading methods, implementations and latest advances," European Journal of Operational Research, Elsevier, vol. 211(3), pages 427-441, June.
    6. Neri Volpato & Lauro Cesar Galvão & Luiz Fernando Nunes & Rômulo Ianuch Souza & Karina Oguido, 2020. "Combining heuristics for tool-path optimisation in material extrusion additive manufacturing," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 71(6), pages 867-877, June.
    7. Cacchiani, Valentina & Contreras-Bolton, Carlos & Toth, Paolo, 2020. "Models and algorithms for the Traveling Salesman Problem with Time-dependent Service times," European Journal of Operational Research, Elsevier, vol. 283(3), pages 825-843.
    8. Taillard, Éric D. & Helsgaun, Keld, 2019. "POPMUSIC for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 420-429.
    9. Campbell, James F. & Corberán, Ángel & Plana, Isaac & Sanchis, José M. & Segura, Paula, 2021. "Solving the length constrained K-drones rural postman problem," European Journal of Operational Research, Elsevier, vol. 292(1), pages 60-72.
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