IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v50y2002i5p862-877.html
   My bibliography  Save this article

A Multilevel Approach to the Travelling Salesman Problem

Author

Listed:
  • Chris Walshaw

    (Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, Greenwich, London, SE10 9LS, United Kingdom)

Abstract

We motivate, derive, and implement a multilevel approach to the travelling salesman problem. The resulting algorithm progressively coarsens the problem, initialises a tour, and then employs either the Lin-Kernighan (LK) or the Chained Lin-Kernighan (CLK) algorithm to refine the solution on each of the coarsened problems in reverse order. In experiments on a well-established test suite of 80 problem instances we found multilevel configurations that either improved the tour quality by over 25% as compared to the standard CLK algorithm using the same amount of execution time, or that achieved approximately the same tour quality over seven times more rapidly. Moreover, the multilevel variants seem to optimise far better the more clustered instances with which the LK and CLK algorithms have the most difficulties.

Suggested Citation

  • Chris Walshaw, 2002. "A Multilevel Approach to the Travelling Salesman Problem," Operations Research, INFORMS, vol. 50(5), pages 862-877, October.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:5:p:862-877
    DOI: 10.1287/opre.50.5.862.373
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.50.5.862.373
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.50.5.862.373?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
    ---><---

    References listed on IDEAS

    as
    1. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    2. Jon Jouis Bentley, 1992. "Fast Algorithms for Geometric Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 4(4), pages 387-411, November.
    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. G. A. Croes, 1958. "A Method for Solving Traveling-Salesman Problems," Operations Research, INFORMS, vol. 6(6), pages 791-812, December.
    6. William Cook & André Rohe, 1999. "Computing Minimum-Weight Perfect Matchings," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 138-148, May.
    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. 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.
    2. Shengbin Wang & Weizhen Rao & Yuan Hong, 2020. "A distance matrix based algorithm for solving the traveling salesman problem," Operational Research, Springer, vol. 20(3), pages 1505-1542, September.
    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.

    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. 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.
    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. 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.
    4. Luc Muyldermans & Patrick Beullens & Dirk Cattrysse & Dirk Van Oudheusden, 2005. "Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem," Operations Research, INFORMS, vol. 53(6), pages 982-995, December.
    5. Sheldon H. Jacobson & Shane N. Hall & Laura A. McLay & Jeffrey E. Orosz, 2005. "Performance Analysis of Cyclical Simulated Annealing Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 183-201, June.
    6. Lucas García & Pedro M. Talaván & Javier Yáñez, 2022. "The 2-opt behavior of the Hopfield Network applied to the TSP," Operational Research, Springer, vol. 22(2), pages 1127-1155, April.
    7. Yannis Marinakis & Athanasios Migdalas & Panos M. Pardalos, 2005. "A Hybrid Genetic—GRASP Algorithm Using Lagrangean Relaxation for the Traveling Salesman Problem," Journal of Combinatorial Optimization, Springer, vol. 10(4), pages 311-326, December.
    8. 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.
    9. 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.
    10. Luca Maria Gambardella & Marco Dorigo, 2000. "An Ant Colony System Hybridized with a New Local Search for the Sequential Ordering Problem," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 237-255, August.
    11. Francesco Carrabs & Jean-François Cordeau & Gilbert Laporte, 2007. "Variable Neighborhood Search for the Pickup and Delivery Traveling Salesman Problem with LIFO Loading," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 618-632, November.
    12. J Renaud & F F Boctor & G Laporte, 2004. "Efficient heuristics for Median Cycle Problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 179-186, February.
    13. Marcel Turkensteen & Dmitry Malyshev & Boris Goldengorin & Panos M. Pardalos, 2017. "The reduction of computation times of upper and lower tolerances for selected combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 68(3), pages 601-622, July.
    14. William Cook & André Rohe, 1999. "Computing Minimum-Weight Perfect Matchings," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 138-148, May.
    15. Daniel Martins & Gabriel M. Vianna & Isabel Rosseti & Simone L. Martins & Alexandre Plastino, 2018. "Making a state-of-the-art heuristic faster with data mining," Annals of Operations Research, Springer, vol. 263(1), pages 141-162, April.
    16. A. S. Santos & A. M. Madureira & M. L. R. Varela, 2018. "The Influence of Problem Specific Neighborhood Structures in Metaheuristics Performance," Journal of Mathematics, Hindawi, vol. 2018, pages 1-14, July.
    17. Scianna, Marco, 2024. "The AddACO: A bio-inspired modified version of the ant colony optimization algorithm to solve travel salesman problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 357-382.
    18. 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.
    19. Yuan Sun & Andreas Ernst & Xiaodong Li & Jake Weiner, 2021. "Generalization of machine learning for problem reduction: a case study on travelling salesman problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 607-633, September.
    20. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Other publications TiSEM ed028a07-eb6a-4c8d-8f21-d, Tilburg University, School of Economics and Management.

    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:inm:oropre:v:50:y:2002:i:5:p:862-877. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.