IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v62y2011i2d10.1057_jors.2010.116.html
   My bibliography  Save this article

Revisiting the big valley search space structure in the TSP

Author

Listed:
  • D R Hains

    (Colorado State University)

  • L D Whitley

    (Colorado State University)

  • A E Howe

    (Colorado State University)

Abstract

The solution space of the travelling salesman problem under 2-opt moves has been characterized as having a big-valley structure, in which the evaluation of a tour is positively correlated to the distance of the tour from the global optimum. We examine the big-valley hypothesis more closely and show that while the big-valley structure does appear in much of the solution space, it breaks down around local optima that have solutions whose evaluation is very close to that of the global optimum; multiple funnels appear around local optima with evaluations close to the global optimum. The appearance of multiple funnels explains why certain iterated local search heuristics can quickly find high-quality solutions, but fail to consistently find the global optimum. We then investigate a novel search operator, which is demonstrated to have the ability to escape funnels at evaluations close to the global optimum.

Suggested Citation

  • D R Hains & L D Whitley & A E Howe, 2011. "Revisiting the big valley search space structure in the TSP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(2), pages 305-312, February.
    • Handle: RePEc:pal:jorsoc:v:62:y:2011:i:2:d:10.1057_jors.2010.116
    DOI: 10.1057/jors.2010.116
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/jors.2010.116
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/jors.2010.116?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. 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.
    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. Mohamad Alissa & Kevin Sim & Emma Hart, 2023. "Automated Algorithm Selection: from Feature-Based to Feature-Free Approaches," Journal of Heuristics, Springer, vol. 29(1), pages 1-38, February.
    2. 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.
    3. Gabriela Ochoa & Nadarajen Veerapen, 2018. "Mapping the global structure of TSP fitness landscapes," Journal of Heuristics, Springer, vol. 24(3), pages 265-294, June.

    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. Ahmed Kheiri & Alina G. Dragomir & David Mueller & Joaquim Gromicho & Caroline Jagtenberg & Jelke J. Hoorn, 2019. "Tackling a VRP challenge to redistribute scarce equipment within time windows using metaheuristic algorithms," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 561-595, December.
    2. Anurag Agarwal, 2009. "Theoretical insights into the augmented-neural-network approach for combinatorial optimization," Annals of Operations Research, Springer, vol. 168(1), pages 101-117, April.
    3. 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.
    4. Aritra Pal & Hadi Charkhgard, 2019. "A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 115-133, February.
    5. 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.
    6. Stefan Poikonen & Bruce Golden, 2020. "The Mothership and Drone Routing Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 249-262, April.
    7. Jung, Jung Woo & Lee, Young Hae, 2010. "Heuristic algorithms for production and transportation planning through synchronization of a serial supply chain," International Journal of Production Economics, Elsevier, vol. 124(2), pages 433-447, April.
    8. R Torres-Velázquez & V Estivill-Castro, 2004. "Local search for Hamiltonian Path with applications to clustering visitation paths," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(7), pages 737-748, July.
    9. 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.
    10. Paolo Gianessi & Laurent Alfandari & Lucas Létocart & Roberto Wolfler Calvo, 2016. "The Multicommodity-Ring Location Routing Problem," Transportation Science, INFORMS, vol. 50(2), pages 541-558, May.
    11. Rego, Cesar & Roucairol, Catherine, 1995. "Using Tabu search for solving a dynamic multi-terminal truck dispatching problem," European Journal of Operational Research, Elsevier, vol. 83(2), pages 411-429, June.
    12. Wayne Desarbo, 1982. "Gennclus: New models for general nonhierarchical clustering analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 449-475, December.
    13. Xuanjing Fang & Yanan Du & Yuzhuo Qiu, 2017. "Reducing Carbon Emissions in a Closed-Loop Production Routing Problem with Simultaneous Pickups and Deliveries under Carbon Cap-and-Trade," Sustainability, MDPI, vol. 9(12), pages 1-15, November.
    14. E A Silver, 2004. "An overview of heuristic solution methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 936-956, September.
    15. Karen Aardal & Cor Hurkens & Jan Karel Lenstra & Sergey Tiourine, 2002. "Algorithms for Radio Link Frequency Assignment: The Calma Project," Operations Research, INFORMS, vol. 50(6), pages 968-980, December.
    16. Ghosh, Diptesh, 2016. "Exploring Lin Kernighan neighborhoods for the indexing problem," IIMA Working Papers WP2016-02-13, Indian Institute of Management Ahmedabad, Research and Publication Department.
    17. Wex, Felix & Schryen, Guido & Feuerriegel, Stefan & Neumann, Dirk, 2014. "Emergency response in natural disaster management: Allocation and scheduling of rescue units," European Journal of Operational Research, Elsevier, vol. 235(3), pages 697-708.
    18. Katayama, Kengo & Narihisa, Hiroyuki, 2001. "Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem," European Journal of Operational Research, Elsevier, vol. 134(1), pages 103-119, October.
    19. Tino Henke & M. Grazia Speranza & Gerhard Wäscher, 2014. "The Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes," FEMM Working Papers 140006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    20. Skålnes, Jørgen & Ben Ahmed, Mohamed & Hvattum, Lars Magnus & Stålhane, Magnus, 2024. "New benchmark instances for the inventory routing problem," European Journal of Operational Research, Elsevier, vol. 313(3), pages 992-1014.

    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:62:y:2011:i:2:d:10.1057_jors.2010.116. 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.