Solving the Traveling Tournament Problem with Predefined Venues by Parallel Constraint Programming

  • Ke LiuEmail author
  • Sven Löffler
  • Petra Hofstedt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11308)


The Traveling Tournament Problem with Predefined Venues (TTPPV) is a practical problem arising from sports scheduling. We describe two different modeling approaches for this problem, each of which is suitable for different sizes of instance. The experimental results show that our modeling approaches lead to improved performance compared to previous techniques in terms of the number of feasible solutions and the optimal value. Furthermore, we present how to execute the models in parallel through data-level parallelism. The parallel versions do not only gain speedup but also attain significant improvement on optimal value since more subtrees are searched independently.


Sports scheduling Constraint programming Parallel constraint solving TTPPV 


  1. 1.
    Pesant, G.: CSPLib: a problem library for constraints. Accessed 08 Apr 2018Google Scholar
  2. 2.
    Melo, R.A., Urrutiá, S., Ribeiro, C.C.: The traveling tournament problem with predefined venues. J. Sched. 12(6), 607–622 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Kendall, G., Knust, S., Ribeiro, C.C., Urrutia, S.: Scheduling in sports: an annotated bibliography. Comput. Oper. Res. 37(1), 1–19 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Tsang, E.: Foundations of Constraint Satisfaction. Academic Press, Boston (1995)Google Scholar
  5. 5.
    Rossi, F., Van Beek, P., Walsh, T.: Handbook of Constraint Programming. Elsevier, New York (2006)zbMATHGoogle Scholar
  6. 6.
    Lecoutre, C.: STR2: optimized simple tabular reduction for table constraints. Constraints 16(4), 341–371 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Prud’homme, C., Fages, J.-G., Lorca, X.: Choco Documentation. TASC - LS2N CNRS UMR 6241, COSLING S.A.S. (2017)Google Scholar
  8. 8.
    Lecoutre, C.: Constraint Networks: Techniques and Algorithms. Wiley, Hoboken (2009)CrossRefGoogle Scholar
  9. 9.
    Pesant, G.: A constraint programming approach to the traveling tournament problem with predefined venues. In: Practice and Theory of Automated Timetabling, pp. 303–316 (2012)Google Scholar
  10. 10.
    Zanarini, A., Pesant, G.: More robust counting-based search heuristics with alldifferent constraints. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 354–368. Springer, Heidelberg (2010). Scholar
  11. 11.
    Régin, J.-C., Rezgui, M., Malapert, A.: Embarrassingly parallel search. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 596–610. Springer, Heidelberg (2013). Scholar
  12. 12.
    Smith, B.M.: Modelling. In: Foundations of Artificial Intelligence, vol. 2, pp. 377–406. Elsevier, Amsterdam (2006)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceBrandenburg University of Technology Cottbus-SenftenbergCottbusGermany

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