Journal of Heuristics

, Volume 13, Issue 2, pp 189–207 | Cite as

A composite-neighborhood tabu search approach to the traveling tournament problem

  • Luca Di Gaspero
  • Andrea Schaerf


The Traveling Tournament Problem (TTP) is a combinatorial problem that combines features from the traveling salesman problem and the tournament scheduling problem. We propose a family of tabu search solvers for the solution of TTP that make use of complex combination of many neighborhood structures. The different neighborhoods have been thoroughly analyzed and experimentally compared. We evaluate the solvers on three sets of publicly available benchmarks and we show a comparison of their outcomes with previous results presented in the literature. The results show that our algorithm is competitive with those in the literature.


Tabu search Local search Composite neighborhood Traveling tournament Tournament scheduling Traveling salesman 


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  1. Ahuja, R.K., J.B. Orin, and D. Sharma. (2000). “Very Large Scale Neighborhood Search.” International Transactions in Operations Research 7, 301–317.CrossRefGoogle Scholar
  2. Anagnostopoulos, A., L. Michel, P. Van Hentenryck, and Y. Vergados. (2005). “A Simulated Annealing Approach to the Traveling Tournament Problem.” Journal of Scheduling 9(2), 177–193.Google Scholar
  3. Araùjo, A., V. Rebello, C. Ribeiro, and S. Urrutia. (2005). “A Grid Implementation of a GRASP”-ILS Heuristic for the Mirrored Traveling Tournament Problem (Extended Abstract). In Proceedings of the 6th Metaheuristics International Conference (MIC2005), Vienna, Austria, pp. 70–76.Google Scholar
  4. Birattari, M. (2004). The Problem of Tuning Metaheuristics as Seen from a Machine Learning Perspective. Ph.D. thesis, Université Libre de Bruxelles, Brussels, Belgium.Google Scholar
  5. Birattari, M. (2005). The RACE Pacakge. Scholar
  6. Conover, W. (1999). Practical Nonparametric Statistics 3rd edn. John Wiley & Sons, New York, NY, USA.Google Scholar
  7. de Werra, D. (1981). “Scheduling in Sports.” In P. Hansen (ed.), Studies on Graphs and Discrete Programming, North Holland, Amsterdam, the Netherlands, pp. 381–395.Google Scholar
  8. Di Gaspero, L. and A. Schaerf. (2003). “ EasyLocal++”: An Object-Oriented Framework for Flexible Design of Local Search Algorithms.” Software—Practice & Experience 33(8), 733–765.CrossRefGoogle Scholar
  9. Dinitz, J.H., D.K. Garnick, and B.D. McKay. (1994). “There are 526,915,620 Nonisomorphic One-factorizations of K 12”. Journal of Combinatorial Design 2, 273–285.MATHMathSciNetGoogle Scholar
  10. Easton, K., G. Nemhauser, and M. Trick. (2001). “The Traveling Tournament Problem Description and Benchmarks.” In Proceedings of the 7th International Conference on the Principles and Practice of Constraint Programming (CP-99), Springer-Verlag, Berlin, Germany, vol. 2239 of Lecture Notes in Computer Science, pp. 580–589.Google Scholar
  11. Easton, K., G. Nemhauser, and M. Trick. (2003). “Solving the Traveling Tournament Problem: A Combined Integer Programming and Constraint Programming Approach.” Practice and Theory of Automated Timetabling IV (PATAT-2002), Springer-Verlag, Berlin, Germany, vol. 2740 of Lecture Notes in Computer Science, pp. 100–109.Google Scholar
  12. Glover, F. and M. Laguna. (1997). Tabu Search. Kluwer Academic Publishers, Norwell, MA, USA.MATHGoogle Scholar
  13. Hansen, P. and N. Mladenovié. (1999). “An Introduction to Variable Neighbourhood Search.” In S. Voß, S. Martello, I. Osman, and C. Roucairol (eds.), Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, Kluwer Academic Publishers, Norwell, MA, USA, pp. 433–458.Google Scholar
  14. Henz, M. (2001). “Scheduling a Major College Basketball Conference—Revisited.” Operations Research 49(1), 163–168.CrossRefMathSciNetGoogle Scholar
  15. Jünger, M., O. Reinelt, and G. Rinaldi. (1995). “The Traveling Salesman Problem.” In M. Ball, T. Magnanti, C. Monma, and G. Nemhauser (eds.), Handbooks in Operations Research and Management Science, North-Holland, Amsterdam, the Netherlands, chapter 7, pp. 225–330.Google Scholar
  16. Langford, G. (2005). “Personal Communication.”Google Scholar
  17. Lim, A., B. Rodrigues, and X. Zhang. (2005). “A Simulated Annealing and Hill-Climbing Algorithm for the Traveling Tournament Problem.” European Journal of Operations Research (to appear).Google Scholar
  18. Lindner, C.C., E. Mendelsohn, and A. Rosa. (1976). “On the Number of 1-Factorizations of the Complete Graph.” Journal of Combinatorial Theory Series B 20, 265–282.MATHCrossRefMathSciNetGoogle Scholar
  19. Lourenço, H.R., O. Martin, and T. Stützle. (2002). “Applying Iterated Local Search to the Permutation flow Shop Problem.” In F. Glover and G. Kochenberger (eds.), Handbook of Metaheuristics, Kluwer Academic Publishers, Norwell, MA, USA, pp. 321–353.Google Scholar
  20. Mendelsohn, E. and A. Rosa. (1985). “One-Factorizations of the Complete Graph—a Survey.” Journal of Graph Theory 9, 43–65.MATHMathSciNetGoogle Scholar
  21. R Development Core Team. (2005). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria., ISBN 3-900051-07-0.Google Scholar
  22. Rasmussen, R. and M. Trick. (2005). “A Benders Approach for the Constrained Minimum Break Problems.” European Journal of Operations Research To appear.Google Scholar
  23. Ribeiro, C.C. and S. Urrutia. (2004). “Heuristics for the Mirrored Traveling Tournament Problem.” In E. Burke and M.A. Trick (eds.), Proceedings of the 5th International Conference on Practice and Theory of Automated Timetabling (PATAT-2004), pp. 323–342.Google Scholar
  24. Schaerf, A. (1999). “Scheduling Sport Tournaments using Constraint Logic Programming.” CONSTRAINTS 4(1), 43–65.MATHCrossRefMathSciNetGoogle Scholar
  25. Trick, M. (2005). “Challenge Traveling Tournament Instances, web page.” URL: Viewed: November 25, 2005, Updated: October 13, 2005.Google Scholar
  26. Urrutia, S. and C.C. Ribeiro. (2005). “Mazimizing Breaks and Bounding Solutions to the Mirrored Traveling Tournament Problem.” Discrete Applied Mathematics154(13), 1932–1938Google Scholar
  27. Wallis, W.D., A.P. Street, and J.S. Wallis. (1972). Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices. Number 292 in Lecture Notes in Mathematics, Springer-Verlag, Berlin, Germany.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria Elettrica, Gestionale e MeccanicaUniversità di UdineUdineItaly

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