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On the Neighborhood Structure of the Traveling Salesman Problem Generated by Local Search Moves

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Abstract

When trying to find approximate solutions for the Traveling Salesman Problem with heuristic optimization algorithms, small moves called Lin-k-Opts are often used. In our paper, we provide exact formulas for the numbers of possible tours into which a randomly chosen tour can be changed with a Lin-k-Opt. Furthermore, we compare the quality of the results to which the various moves lead.

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Authors and Affiliations

  1. Computer Science, Fernfachhochschule Schweiz, Überlandstr. 12, Postfach 689, 3900, Brig, Switzerland

    Günther Stattenberger

  2. Independent IT Consultant, Ed.-Mühlbauer-Weg 14, 93051, Regensburg, Germany

    Markus Dankesreiter

  3. Swisscom Innovations, Swisscom, Ostermundigenstr. 93, 3006, Berne, Switzerland

    Florian Baumgartner

  4. Institute of Physics, Johannes Gutenberg University of Mainz, Staudinger Weg 7, 55099, Mainz, Germany

    Johannes J. Schneider

Authors
  1. Günther Stattenberger
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  2. Markus Dankesreiter
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  3. Florian Baumgartner
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  4. Johannes J. Schneider
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Correspondence to Johannes J. Schneider.

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Stattenberger, G., Dankesreiter, M., Baumgartner, F. et al. On the Neighborhood Structure of the Traveling Salesman Problem Generated by Local Search Moves. J Stat Phys 129, 623–648 (2007). https://doi.org/10.1007/s10955-007-9382-1

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  • DOI: https://doi.org/10.1007/s10955-007-9382-1

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