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Improving the Efficiency of Helsgaun’s Lin-Kernighan Heuristic for the Symmetric TSP

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Book cover Combinatorial and Algorithmic Aspects of Networking (CAAN 2007)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 4852))

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Abstract

Helsgaun has introduced and implemented the lower tolerances (α-values) for an approximation of Held-Karp’s 1-tree with the purpose to improve the Lin-Kernighan Heuristic (LKH) for the Symmetric TSP (STSP). The LKH appears to exceed the performance of all STSP heuristic algorithms proposed to date.

In this paper we improve Helsgaun’s LKH based on an approximation of Zhang and Looks’ backbones and an extension of double bridges further combined with implementation details by all of which we guide the search process instead of Helsgaun’s α-values. Our computational results are competitive and lead to improved solutions for some of the VLSI instances announced at the TSP homepage.

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Authors and Affiliations

  1. Computer Science Institute, University of Halle-Wittenberg, D-06099, Halle(Saale), Germany

    Dirk Richter & Paul Molitor

  2. Faculty of Economic Sciences, University of Groningen, 9700 AV, Groningen, The Netherlands

    Boris Goldengorin

  3. University of Economics and Business, Lviv Highway 51/2, 29016, Khmelnitsky, Ukraine

    Boris Goldengorin

  4. Department of Applied Mathematics, Khmelnitsky National University, Ukraine

    Boris Goldengorin

  5. Department of Computer Science, Washington University, Campus Box 1045, One Brookings Drive, St. Louis, Missouri, 63130-4899, USA

    Gerold Jäger

Authors
  1. Dirk Richter
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  2. Boris Goldengorin
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  3. Gerold Jäger
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  4. Paul Molitor
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Jeannette Janssen Paweł Prałat

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Richter, D., Goldengorin, B., Jäger, G., Molitor, P. (2007). Improving the Efficiency of Helsgaun’s Lin-Kernighan Heuristic for the Symmetric TSP . In: Janssen, J., Prałat, P. (eds) Combinatorial and Algorithmic Aspects of Networking. CAAN 2007. Lecture Notes in Computer Science, vol 4852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77294-1_10

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  • DOI: https://doi.org/10.1007/978-3-540-77294-1_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77293-4

  • Online ISBN: 978-3-540-77294-1

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