IDEAS home Printed from https://ideas.repec.org/p/jgu/wpaper/2020.html
   My bibliography  Save this paper

New Neighborhoods and an Iterated Local Search Algorithm for the Generalized Traveling Salesman Problem

Author

Listed:
  • Jeanette Schmidt

    (Johannes Gutenberg University)

  • Stefan Irnich

    (Johannes Gutenberg University)

Abstract

The generalized traveling salesman problem (GTSP) is the problem of finding a cost-minimal cycle in a clustered graph so that exactly one vertex of every cluster is contained in the cycle. We introduce three new GTSP neighborhoods that allow the simultaneous permutation of the sequence of the clusters and the selection of vertices from each cluster. The three neighborhoods and some known neighborhoods from the literature are combined into a simple but effective iterated local search (ILS) for the GTSP. The simplicity of the ILS consists in its straightforward random neighborhood selection within the local search and an ordinary record-to-record ILS acceptance criterion. The computational experiments on four symmetric standard GTSP libraries show that, with some small refinements, the ILS can compete with state-of-the-art algorithms, although it is simple in structure and less involved to code compared to many other metaheuristics.

Suggested Citation

  • Jeanette Schmidt & Stefan Irnich, 2020. "New Neighborhoods and an Iterated Local Search Algorithm for the Generalized Traveling Salesman Problem," Working Papers 2020, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
  • Handle: RePEc:jgu:wpaper:2020
    as

    Download full text from publisher

    File URL: https://download.uni-mainz.de/RePEc/pdf/Discussion_Paper_2020.pdf
    File Function: First version, 2020
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Karapetyan, D. & Gutin, G., 2011. "Lin-Kernighan heuristic adaptations for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 208(3), pages 221-232, February.
    2. Renaud, Jacques & Boctor, Fayez F., 1998. "An efficient composite heuristic for the symmetric generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 108(3), pages 571-584, August.
    3. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    4. 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.
    5. Karapetyan, D. & Gutin, G., 2012. "Efficient local search algorithms for known and new neighborhoods for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 219(2), pages 234-251.
    6. Helsgaun, Keld, 2000. "An effective implementation of the Lin-Kernighan traveling salesman heuristic," European Journal of Operational Research, Elsevier, vol. 126(1), pages 106-130, October.
    7. Charles E. Noon & James C. Bean, 1991. "A Lagrangian Based Approach for the Asymmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 39(4), pages 623-632, August.
    8. Jean Bertrand Gauthier & Stefan Irnich, 2020. "Inter-Depot Moves and Dynamic-Radius Search for Multi-Depot Vehicle Routing Problems," Working Papers 2004, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    9. Jon Jouis Bentley, 1992. "Fast Algorithms for Geometric Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 4(4), pages 387-411, November.
    10. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    11. E. Balas, 1999. "New classes of efficiently solvable generalized Traveling Salesman Problems," Annals of Operations Research, Springer, vol. 86(0), pages 529-558, January.
    12. Paolo Toth & Daniele Vigo, 2003. "The Granular Tabu Search and Its Application to the Vehicle-Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 333-346, November.
    13. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    14. Egon Balas & Neil Simonetti, 2001. "Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study," INFORMS Journal on Computing, INFORMS, vol. 13(1), pages 56-75, February.
    15. Snyder, Lawrence V. & Daskin, Mark S., 2006. "A random-key genetic algorithm for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 174(1), pages 38-53, October.
    Full references (including those not matched with items on IDEAS)

    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. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.
    2. Bruce Golden & Zahra Naji-Azimi & S. Raghavan & Majid Salari & Paolo Toth, 2012. "The Generalized Covering Salesman Problem," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 534-553, November.
    3. Mehdi El Krari & Belaïd Ahiod & Youssef Bouazza El Benani, 2021. "A pre-processing reduction method for the generalized travelling salesman problem," Operational Research, Springer, vol. 21(4), pages 2543-2591, December.
    4. Karapetyan, D. & Gutin, G., 2011. "Lin-Kernighan heuristic adaptations for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 208(3), pages 221-232, February.
    5. 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.
    6. 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.
    7. Hintsch, Timo & Irnich, Stefan, 2018. "Large multiple neighborhood search for the clustered vehicle-routing problem," European Journal of Operational Research, Elsevier, vol. 270(1), pages 118-131.
    8. Gharehgozli, Amir & Yu, Yugang & de Koster, René & Du, Shaofu, 2019. "Sequencing storage and retrieval requests in a container block with multiple open locations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 125(C), pages 261-284.
    9. Timo Hintsch & Stefan Irnich, 2017. "Large Multiple Neighborhood Search for the Clustered Vehicle-Routing Problem," Working Papers 1701, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    10. William Cook & Paul Seymour, 2003. "Tour Merging via Branch-Decomposition," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 233-248, August.
    11. Muren, & Wu, Jianjun & Zhou, Li & Du, Zhiping & Lv, Ying, 2019. "Mixed steepest descent algorithm for the traveling salesman problem and application in air logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 87-102.
    12. Karapetyan, D. & Gutin, G., 2012. "Efficient local search algorithms for known and new neighborhoods for the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 219(2), pages 234-251.
    13. Baniasadi, Pouya & Foumani, Mehdi & Smith-Miles, Kate & Ejov, Vladimir, 2020. "A transformation technique for the clustered generalized traveling salesman problem with applications to logistics," European Journal of Operational Research, Elsevier, vol. 285(2), pages 444-457.
    14. Amir Hossein Gharehgozli & Gilbert Laporte & Yugang Yu & René de Koster, 2015. "Scheduling Twin Yard Cranes in a Container Block," Transportation Science, INFORMS, vol. 49(3), pages 686-705, August.
    15. Jean Bertrand Gauthier & Stefan Irnich, 2020. "Inter-Depot Moves and Dynamic-Radius Search for Multi-Depot Vehicle Routing Problems," Working Papers 2004, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    16. Chris Walshaw, 2002. "A Multilevel Approach to the Travelling Salesman Problem," Operations Research, INFORMS, vol. 50(5), pages 862-877, October.
    17. Timo Hintsch, 2019. "Large Multiple Neighborhood Search for the Soft-Clustered Vehicle-Routing Problem," Working Papers 1904, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    18. K Sang-Ho & G Young-Gun & K Maing-Kyu, 2003. "Application of the out-of-kilter algorithm to the asymmetric traveling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(10), pages 1085-1092, October.
    19. Rajabighamchi, Farzaneh & van Hoesel, Stan & Defryn, Christof, 2023. "The order picking problem under a scattered storage policy," Research Memorandum 006, Maastricht University, Graduate School of Business and Economics (GSBE).
    20. G Babin & S Deneault & G Laporte, 2007. "Improvements to the Or-opt heuristic for the symmetric travelling salesman problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(3), pages 402-407, March.

    More about this item

    Keywords

    traveling salesman; generalized traveling salesman problem; iterated local search; variable neighborhood descent;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:jgu:wpaper:2020. 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: Research Unit IPP (email available below). General contact details of provider: https://edirc.repec.org/data/vlmaide.html .

    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.