IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v54y2003i10d10.1057_palgrave.jors.2601614.html
   My bibliography  Save this article

Application of the out-of-kilter algorithm to the asymmetric traveling salesman problem

Author

Listed:
  • K Sang-Ho

    (Hanyang University, Sa-dong, Ansan)

  • G Young-Gun

    (Hanyang University, Sa-dong, Ansan)

  • K Maing-Kyu

    (Hanyang University, Sa-dong, Ansan)

Abstract

This paper presents a heuristic method that finds optimum or near-optimum solutions to the asymmetric traveling salesman problem. The method uses the out-of-kilter algorithm to search for a neighbourhood. When subtours are produced by a flow-augmenting path of the out-of-kilter algorithm, it patches them into a Hamiltonian cycle. It extends the neighbourhood space by exchanging an even number of arcs, and it also exchanges arcs by a non-sequential primary change. Instances from real applications were used to test the algorithm, along with randomly generated problems. The new heuristic algorithm produced optimum solutions for 16 out of 28 real-world instances from TSPLIB and other sources. Also, compared with four efficient heuristics, it produced the best solutions for all except six instances. It also produced relatively good solutions in reasonable times for 216 randomly generated instances from nine instance generators.

Suggested Citation

  • 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.
  • Handle: RePEc:pal:jorsoc:v:54:y:2003:i:10:d:10.1057_palgrave.jors.2601614
    DOI: 10.1057/palgrave.jors.2601614
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2601614
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1057/palgrave.jors.2601614?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. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    2. 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.
    3. 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.
    4. Paris-C. Kanellakis & Christos H. Papadimitriou, 1980. "Local Search for the Asymmetric Traveling Salesman Problem," Operations Research, INFORMS, vol. 28(5), pages 1086-1099, 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. 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. 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.
    3. 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.
    4. 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.
    5. William Cook & Paul Seymour, 2003. "Tour Merging via Branch-Decomposition," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 233-248, August.
    6. L Vogt & C A Poojari & J E Beasley, 2007. "A tabu search algorithm for the single vehicle routing allocation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 467-480, April.
    7. Burger, M. & Su, Z. & De Schutter, B., 2018. "A node current-based 2-index formulation for the fixed-destination multi-depot travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 463-477.
    8. 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.
    9. 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.
    10. 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.
    11. Jean-Charles Créput & Amir Hajjam & Abderrafiaa Koukam & Olivier Kuhn, 2012. "Self-organizing maps in population based metaheuristic to the dynamic vehicle routing problem," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 437-458, November.
    12. Nikolakopoulos, Athanassios & Sarimveis, Haralambos, 2007. "A threshold accepting heuristic with intense local search for the solution of special instances of the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1911-1929, March.
    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. 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.
    15. Mauro Dell’Amico & Roberto Montemanni & Stefano Novellani, 2020. "Matheuristic algorithms for the parallel drone scheduling traveling salesman problem," Annals of Operations Research, Springer, vol. 289(2), pages 211-226, June.
    16. 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.
    17. 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.
    18. Chen, Yu-Wang & Zhu, Yao-Jia & Yang, Gen-Ke & Lu, Yong-Zai, 2011. "Improved extremal optimization for the asymmetric traveling salesman problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4459-4465.
    19. William Cook & Daniel G. Espinoza & Marcos Goycoolea, 2007. "Computing with Domino-Parity Inequalities for the Traveling Salesman Problem (TSP)," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 356-365, August.
    20. 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.

    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:pal:jorsoc:v:54:y:2003:i:10:d:10.1057_palgrave.jors.2601614. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    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.