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Branch-and-Bound Algorithm for Symmetric Travelling Salesman Problem

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Combinatorial Algorithms (IWOCA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10979))

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Abstract

In this paper a branch-and-bound algorithm for the Symmetric Travelling Salesman Problem (STSP) is presented. The algorithm is based on the 1-tree Lagrangian relaxation. A new branching strategy is suggested in which the algorithm branches on the 1-tree edge belonging to the vertex with maximum degree in the 1-tree and having the maximum tolerance. This strategy is compared with branching on the shortest edge and the so-called strong branching, which is the branching on the edge with maximum tolerance also applied by Held and Karp (1971). The computational experiments show that proposed branching strategy provides better results on TSPlib benchmark instances.

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References

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Acknowledgments

The research was funded by Russian Science Foundation (RSF project No. 17-71-10107).

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Authors and Affiliations

  1. Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, 136 Rodionova street, Nizhny Novgorod, Russia

    Alexey Nikolaev & Mikhail Batsyn

Authors
  1. Alexey Nikolaev
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  2. Mikhail Batsyn
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Corresponding author

Correspondence to Alexey Nikolaev .

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Editors and Affiliations

  1. Department of Informatics, King’s College London, London, United Kingdom

    Costas Iliopoulos

  2. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

    Hon Wai Leong

  3. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

    Wing-Kin Sung

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Nikolaev, A., Batsyn, M. (2018). Branch-and-Bound Algorithm for Symmetric Travelling Salesman Problem. In: Iliopoulos, C., Leong, H., Sung, WK. (eds) Combinatorial Algorithms. IWOCA 2018. Lecture Notes in Computer Science(), vol 10979. Springer, Cham. https://doi.org/10.1007/978-3-319-94667-2_26

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  • DOI: https://doi.org/10.1007/978-3-319-94667-2_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94666-5

  • Online ISBN: 978-3-319-94667-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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