IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v272y2019i2p420-429.html
   My bibliography  Save this article

POPMUSIC for the travelling salesman problem

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718305745
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.06.039?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. William Cook & Paul Seymour, 2003. "Tour Merging via Branch-Decomposition," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 233-248, August.
    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. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    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. Alvim, Adriana C.F. & Taillard, Éric D., 2009. "POPMUSIC for the point feature label placement problem," European Journal of Operational Research, Elsevier, vol. 192(2), pages 396-413, January.
    7. A Ostertag & K F Doerner & R F Hartl & E D Taillard & P Waelti, 2009. "POPMUSIC for a real-world large-scale vehicle routing problem with time windows," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(7), pages 934-943, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Taillard, Éric D., 2022. "A linearithmic heuristic for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 442-450.
    3. 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.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gary R. Waissi & Pragya Kaushal, 2020. "A polynomial matrix processing heuristic algorithm for finding high quality feasible solutions for the TSP," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 73-87, March.
    2. Taillard, Éric D., 2022. "A linearithmic heuristic for the travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 297(2), pages 442-450.
    3. Yuichi Nagata & Shigenobu Kobayashi, 2013. "A Powerful Genetic Algorithm Using Edge Assembly Crossover for the Traveling Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 346-363, May.
    4. Andrzej Jaszkiewicz & Thibaut Lust, 2017. "Proper balance between search towards and along Pareto front: biobjective TSP case study," Annals of Operations Research, Springer, vol. 254(1), pages 111-130, July.
    5. Jiang, Zhongzhou & Liu, Jing & Wang, Shuai, 2016. "Traveling salesman problems with PageRank Distance on complex networks reveal community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 293-302.
    6. Sebastian Herrmann & Gabriela Ochoa & Franz Rothlauf, 2016. "Communities of Local Optima as Funnels in Fitness Landscapes," Working Papers 1609, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    7. Elena Nechita & Gloria Cerasela Crişan & Laszlo Barna Iantovics & Yitong Huang, 2020. "On the Resilience of Ant Algorithms. Experiment with Adapted MMAS on TSP," Mathematics, MDPI, vol. 8(5), pages 1-20, May.
    8. Sleegers, Joeri & Olij, Richard & van Horn, Gijs & van den Berg, Daan, 2020. "Where the really hard problems aren’t," Operations Research Perspectives, Elsevier, vol. 7(C).
    9. repec:jss:jstsof:23:i02 is not listed on IDEAS
    10. William Cook & Paul Seymour, 2003. "Tour Merging via Branch-Decomposition," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 233-248, August.
    11. 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.
    12. Sebastian Herrmann & Gabriela Ochoa & Franz Rothlauf, 2018. "PageRank centrality for performance prediction: the impact of the local optima network model," Journal of Heuristics, Springer, vol. 24(3), pages 243-264, June.
    13. Zhang, Guoqing & Nishi, Tatsushi & Turner, Sarina D.O. & Oga, Keisuke & Li, Xindan, 2017. "An integrated strategy for a production planning and warehouse layout problem: Modeling and solution approaches," Omega, Elsevier, vol. 68(C), pages 85-94.
    14. César Rego & Fred Glover, 2010. "Ejection chain and filter-and-fan methods in combinatorial optimization," Annals of Operations Research, Springer, vol. 175(1), pages 77-105, March.
    15. Çavdar, Bahar & Sokol, Joel, 2015. "TSP Race: Minimizing completion time in time-sensitive applications," European Journal of Operational Research, Elsevier, vol. 244(1), pages 47-54.
    16. Thomas Weise & Yuezhong Wu & Raymond Chiong & Ke Tang & Jörg Lässig, 2016. "Global versus local search: the impact of population sizes on evolutionary algorithm performance," Journal of Global Optimization, Springer, vol. 66(3), pages 511-534, November.
    17. Eduardo Lalla-Ruiz & Stefan Voß & Christopher Expósito-Izquierdo & Belén Melián-Batista & J. Marcos Moreno-Vega, 2017. "A POPMUSIC-based approach for the berth allocation problem under time-dependent limitations," Annals of Operations Research, Springer, vol. 253(2), pages 871-897, June.
    18. Charles, Mehdi & Dauzère-Pérès, Stéphane & Kedad-Sidhoum, Safia & Mazhoud, Issam, 2022. "Motivations and analysis of the capacitated lot-sizing problem with setup times and minimum and maximum ending inventories," European Journal of Operational Research, Elsevier, vol. 302(1), pages 203-220.
    19. Sereshti, Narges & Adulyasak, Yossiri & Jans, Raf, 2024. "Managing flexibility in stochastic multi-level lot sizing problem with service level constraints," Omega, Elsevier, vol. 122(C).
    20. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    21. Zi-bin Jiang & Qiong Yang, 2016. "A Discrete Fruit Fly Optimization Algorithm for the Traveling Salesman Problem," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-15, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:272:y:2019:i:2:p:420-429. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.