Abstract

Our paper presents a new exact method to solve the traveling tournament problem. More precisely, we apply DFS* to this problem and improve its performance by keeping the expensive heuristic estimates in memory to help greatly cut down the computational time needed. We further improve the performance by exploiting a symmetry property found in the traveling tournament problem. Our results show that our approach is one of the top performing approaches for this problem. It is able to find known optimal solutions in a much smaller amount of computational time than past approaches, to find a new optimal solution, and to improve the lower bounds of larger problem instances which do not have known optimal solutions. As a final contribution, we also introduce a new set of problem instances to diversify the available instance sets for the traveling tournament problem.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benoist, T., Laburthe, F., Rottembourg, B.: Lagrange relaxation and constraint programming collaborative schemes for travelling tournament problems. In: Proceedings of CP-AI-OR 2001, Wye College, UK, pp. 15–26 (2001)Google Scholar
  2. 2.
    Dechter, R.: Constraint Processing. Morgan Kaufmann Publishers, San Francisco (2003)MATHGoogle Scholar
  3. 3.
    Easton, K., Nemhauser, G., Trick, M.: The traveling tournament problem description and benchmarks. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–584. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Easton, K., Nemhauser, G., Trick, M.: Solving the travelling tournament problem: A combined integer programming and constraint programming approach. In: Burke, E.K., De Causmaecker, P. (eds.) PATAT 2002. LNCS, vol. 2740, pp. 100–109. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Irnich, S., Schrempp, U.: A new branch-and-price algorithm for the traveling tournament problem. Presented at Column Generation 2008, Aussois, France (June 17-20, 2008), http://www.gerad.ca/colloques/ColumnGeneration2008/slides/SIrnich.pdf (accessed March 07, 2009)
  6. 6.
    Sarkar, U.K., Chakrabarti, P.P., Ghose, S., De Sarkar, S.C.: Reducing reexpansions in iterative-deepening search by controlling cutoff bounds. Artificial Intelligence 50, 207–221 (1991)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Trick, M.: Challenge Traveling Tournament Problems, http://mat.gsia.cmu.edu/TOURN/ (accessed March 07, 2009)
  8. 8.
    Urrutia, S., Ribeiro, C.C., Melo, R.A.: A new lower bound to the traveling tournament problem. In: IEEE Symposium on Computational Intelligence in Scheduling, pp. 15–18 (2007)Google Scholar
  9. 9.
    Vempaty, N.R., Kumar, V., Korf, R.E.: Depth-First vs Best-First Search. In: Proc. National Conf. on Artificial Intelligence, AAAI 1991, Anaheim, CA, pp. 434–440 (1991)Google Scholar
  10. 10.
    Wah, B.W.: MIDA*: An IDA* search with dynamic control. Technical report, Coordinated Science Laboratoy, University of Illinois, Urbana, Illinois (1991)Google Scholar
  11. 11.
    Talbi, E.-G.: Parallel Combinatorial Optimization. John Wiley & Sons, Hoboken (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • David C. Uthus
    • 1
  • Patricia J. Riddle
    • 1
  • Hans W. Guesgen
    • 2
  1. 1.University of AucklandAucklandNew Zealand
  2. 2.Massey UniversityPalmerston NorthNew Zealand

Personalised recommendations