Mirrored Traveling Tournament Problem: An Evolutionary Approach

  • Fabrício Lacerda Biajoli
  • Luiz Antonio Nogueira Lorena
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4140)


The Mirrored Traveling Tournament Problem (mTTP) is an optimization problem that represents certain types of sports timetabling, where the objective is to minimize the total distance traveled by the teams. This work proposes the use of hybrid heuristic to solve the mTTP, using an evolutionary algorithm in association with the metaheuristic Simulated Annealing. It suggests the use of Genetic Algorithm with a compact genetic codification in conjunction with an algorithm to expand the code. The validation of the results will be done in benchmark problems available in literature and real benchmark problems, e.g. Brazilian Soccer Championship.


Genetic Algorithm Schedule Problem Local Search Simulated Annealing Evolutionary Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anagnostopoulos, A., Michel, L., Van Hentenryck, P., Vergados, Y.: A Simulated Annealing Approach to the Traveling Tournament Problem. In: Proceedings of Cpaior 2003 (2003)Google Scholar
  2. 2.
    Biajoli, F.L., Chaves, A.A., Mine, O.M., Souza, M.J.F., Pontes, R.C., Lucena, A., Cabral, L.F.: Scheduling the Brazilian Soccer Championship: A Simulated Annealing Approach. In: Burke, E.K., Trick, M.A. (eds.) PATAT 2004. LNCS, vol. 3616, pp. 433–437. Springer, Heidelberg (2005)Google Scholar
  3. 3.
    Concílio, R., Zuben, F.J.: Uma Abordagem Evolutiva para Geração Automática de Turnos Completos em Torneios. Revista Controle e Automação 13(2), 105–122 (2002)Google Scholar
  4. 4.
    Costa, D.: An Evolutionary Tabu Search Algorithm and the NHL Scheduling Problem. Infor. 33(3), 161–178 (1995)MATHGoogle Scholar
  5. 5.
    Dinitz, J., Lamken, E., Wallis, W.D.: Scheduling a Tournament. In: Colbourn, C.J., Dinitz, J. (eds.) Handbook of Combinatorial Designs, pp. 578–584. CRC Press, Boca Raton (1995)Google Scholar
  6. 6.
    Dowsland, K.A.: Simulated Annealing. In: Reeves, C.R. (ed.) Modern Heuristic Techniques for Combinatorial Problems, Advanced Topics in Computer Science Series, ch. 2. pp. 20–69. Blackwell Scientific Publications, London (1993)Google Scholar
  7. 7.
    Easton, K., Nemhauser, G., Trick, M.: The Traveling Tournament Problem Description and Benchmarks. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 580–589. Springer, Heidelberg (2000)Google Scholar
  8. 8.
    Goldberg, D.E.: Genetic Algorithms in Search. In: Optimization and Machine Learning, p. 223. Addison-Wesley, Berkeley (1989)Google Scholar
  9. 9.
    Hamiez, J.P., Hao, J.K.: Solving the sports league scheduling problem with tabu search. In: Nareyek, A. (ed.) ECAI-WS 2000. LNCS (LNAI), vol. 2148, pp. 24–36. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Holland, J.H.: Adaptation in Natural and Artificial Systems, p. 211. University of Michigan Press, Ann Arbor (1975)Google Scholar
  11. 11.
    Kirkpatrick, S., Gellat, D.C., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Nemhauser, G., Trick, M.: Scheduling a Major College Basketball Conference. Operations Research 46(1), 1–8 (1998)CrossRefGoogle Scholar
  13. 13.
    Ribeiro, C.C., Urrutia, S.: Heuristics for the Mirrored Traveling Tournament Problem. In: Burke, E.K., Trick, M.A. (eds.) PATAT 2004. LNCS, vol. 3616, pp. 323–342. Springer, Heidelberg (2004)Google Scholar
  14. 14.
    Schönberger, J., Mattfeld, D.C., Kopfer, H.: Memetic Algorithm Timetabling for Non-Commercial Sport Leagues. European Journal of Operational Research 153(1), 102–116 (1989)CrossRefGoogle Scholar
  15. 15.
    Syswerda, G.: Uniform Crossover in Genetic Algorithms. In: International Conference on Genetic Algorithms (ICGA), Virginia, USA, vol. 3, pp. 2–9 (1989)Google Scholar
  16. 16.
    Trick, M.A.: A schedule-then-break approach to sports timetabling. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 242–253. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  17. 17.
    Whitley, D., Gordon, V.S., Mathiask, K.: Lamarckian Evolution, the Baldwin Effect and Function Optimization. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 6–15. Springer, Heidelberg (1994)Google Scholar
  18. 18.
    Zhang, H.: Generating College Conference Basketball Schedules by a Sat Solver. In: Proceedings Of The Fifth International Symposium on the Theory and Applications of Satisfiability Testing, Cincinnati, pp. 281–291 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fabrício Lacerda Biajoli
    • 1
  • Luiz Antonio Nogueira Lorena
    • 1
  1. 1.Laboratório Associado de Computação e Matemática Aplicada – LACInstituto Nacional de Pesquisas Espaciais – INPESão José dos CamposBrazil

Personalised recommendations