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Revisiting the big valley search space structure in the TSP

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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
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    References listed on IDEAS

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    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.
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    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.

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