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)


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.


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



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


  1. Benchimol, P., Régin, J.C., Rousseau, L.M., Rueher, M., van Hoeve, W.J.: Improving the Held and Karp approach with constraint programming. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 40–44. Springer, Heidelberg (2010). Scholar
  2. Hansen, K.H., Krarup, J.: Improvements of the Held-Karp algorithm for the symmetric traveling-salesman problem. Math. Program. 7(1), 87–96 (1974)MathSciNetCrossRefGoogle Scholar
  3. Held, M., Karp, R.M.: The traveling-salesman problem and minimum spanning trees. Oper. Res. 18(6), 1138–1162 (1970)MathSciNetCrossRefGoogle Scholar
  4. Held, M., Karp, R.M.: The traveling-salesman problem and minimum spanning trees: Part II. Math. Program. 1(1), 6–25 (1971)CrossRefGoogle Scholar
  5. Helsgaun, K.: An effective implementation of the Lin-Kernighan traveling salesman heuristic. Eur. J. Oper. Res. 126(1), 106–130 (2000)MathSciNetCrossRefGoogle Scholar
  6. Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59(2), 231–247 (1992)CrossRefGoogle Scholar
  7. Matai, R., Singh, S., Mittal, M.L.: Traveling salesman problem: an overview of applications, formulations, and solution approaches. In: Traveling Salesman Problem, Theory and Applications. InTech (2010)Google Scholar
  8. Reinelt, G.: TSPLIB-A traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)CrossRefGoogle Scholar
  9. Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Lecture Notes in Computer Science. Springer, Heidelberg (1994). Scholar
  10. Volgenant, T., Jonker, R.: A branch and bound algorithm for the symmetric traveling salesman problem based on the 1-tree relaxation. Eur. J. Oper. Res. 9(1), 83–89 (1982)MathSciNetCrossRefGoogle Scholar

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

Personalised recommendations