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Branch-and-Bound Algorithm for Symmetric Travelling Salesman Problem

  • Alexey NikolaevEmail author
  • Mikhail Batsyn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10979)

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.

Keywords

Traveling salesman problem 1-tree Branch-and-bound algorithm 

Notes

Acknowledgments

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

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratory of Algorithms and Technologies for Network AnalysisNational Research University Higher School of EconomicsNizhny NovgorodRussia

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