Finding Good Tours for Huge Euclidean TSP Instances by Iterative Backbone Contraction

  • Christian Ernst
  • Changxing Dong
  • Gerold Jäger
  • Dirk Richter
  • Paul Molitor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6124)


This paper presents an iterative, highly parallelizable approach to find good tours for very large instances of the Euclidian version of the well-known Traveling Salesman Problem (TSP). The basic idea of the approach consists of iteratively transforming the TSP instance to another one with smaller size by contracting pseudo backbone edges. The iteration is stopped, if the new TSP instance is small enough for directly applying an exact algorithm or an efficient TSP heuristic. The pseudo backbone edges of each iteration are computed by a window based technique in which the TSP instance is tiled in non-disjoint sub-instances. For each of these sub-instances a good tour is computed, independently of the other sub-instances. An edge which is contained in the computed tour of every sub-instance (of the current iteration) containing this edge is denoted to be a pseudo backbone edge. Paths of pseudo-backbone edges are contracted to single edges which are fixed during the subsequent process.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J.: The Traveling Salesman Problem. In: A Computational Study. Princeton University Press, Princeton (2006)Google Scholar
  2. 2.
    Applegate, D.L., Bixby, R.E., Chvátal, V., Cook, W.J., Espinoza, D., Goycoolea, M., Helsgaun, K.: Certification of an Optimal Tour through 85,900 Cities. Operations Research Letters 37(1), 11–15 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cook, W., Seymour, P.: Tour Merging via Branch-Decomposition. INFORMS Journal on Computing 15(3), 233–248 (2003)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Dong, C., Jäger, G., Richter, D., Molitor, P.: Effective Tour Searching for TSP by Contraction of Pseudo Backbone Edges. In: Goldberg, A.V., Zhou, Y. (eds.) AAIM 2009. LNCS, vol. 5564, pp. 175–187. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Gutin, G., Punnen, A.P. (eds.): The Traveling Salesman Problem and Its Variations. Kluwer Academic Publishers, Dordrecht (2002)zbMATHGoogle Scholar
  6. 6.
    Helsgaun, K.: An Effective Implementation of the Lin-Kernighan Traveling Salesman Heuristic. European Journal Operations Research 126(1), 106–130 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Helsgaun, K.: An Effective Implementation of k-opt Moves for the Lin-Kernighan TSP Heuristic. In: Writings in Computer Science, vol. 109. Roskilde University (2006)Google Scholar
  8. 8.
    Helsgaun, K.: General k-opt submoves for the Lin-Kernighan TSP heuristic. Mathematical Programming Computation 1(2-3), 119–163 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Helsgaun, K.: Private Communication (March 2009)Google Scholar
  10. 10.
    Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B. (eds.): The Traveling Salesman Problem - A Guided Tour of Combinatorial Optimization. John Wiley & Sons, Chicester (1985)zbMATHGoogle Scholar
  11. 11.
    Lin, S., Kernighan, B.W.: An Effective Heuristic Algorithm for the Traveling Salesman Problem. Operations Research 21, 498–516 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Walshaw, C.: A Multilevel Lin-Kernighan-Helsgaun Algorithm for the Travelling Salesman Problem. TR 01/IM/80, Computing and Mathematical Sciences, University of Greenwich, UK (2001)Google Scholar
  13. 13.
    Zhang, W., Looks, M.: A Novel Local Search Algorithm for the Traveling Salesman Problem that Exploits Backbones. In: Proc. of the 19th Int’l Joint Conf. on Artificial Intelligence (IJCAI 2005), pp. 343–350 (2005)Google Scholar
  14. 14.
  15. 15.
    DIMACS Implementation Challenge,
  16. 16.
  17. 17.
  18. 18.
    VLSI Instances from the TSP Homepage,
  19. 19.
    World-TSP from the TSP Homepage,
  20. 20.
    Source Code of [1] (Concorde),
  21. 21.

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christian Ernst
    • 1
    • 3
  • Changxing Dong
    • 1
  • Gerold Jäger
    • 1
    • 2
  • Dirk Richter
    • 1
  • Paul Molitor
    • 1
  1. 1.Martin-Luther-University Halle-WittenbergHalle (Saale)Germany
  2. 2.Christian-Albrechts-University KielKielGermany
  3. 3.GISA GmbHHalle (Saale)Germany

Personalised recommendations