Scheduling Social Golfers with Memetic Evolutionary Programming

  • Carlos Cotta
  • Iván Dotú
  • Antonio J. Fernández
  • Pascal Van Hentenryck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4030)


The social golfer problem (SGP) has attracted significant attention in recent years because of its highly symmetrical, constrained, and combinatorial nature. Nowadays, it constitutes one of the standard benchmarks in the area of constraint programming. This paper presents the first evolutionary approach to the SGP. We propose a memetic algorithm (MA) that combines ideas from evolutionary programming and tabu search. In order to lessen the influence of the high number of symmetries present in the problem, the MA does not make use of recombination operators. The search is thus propelled by selection, mutation, and local search. In connection with the latter, we analyze the effect of baldwinian and lamarckian learning in the performance of the MA. An experimental study shows that the MA is capable of improving results reported in the literature, and supports the superiority of lamarckian strategies in this problem.


Local Search Tabu Search Constraint Programming Memetic Algorithm Tabu List 
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.
    Fahle, T., Schamberger, S., Sellmann, M.: Symmetry breaking. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 93–107. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Smith, B.M.: Reducing symmetry in a combinatorial design problem. In: Third International Workshop on the Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pp. 351–359 (2001)Google Scholar
  3. 3.
    Sellmann, M., Harvey, W.: Heuristic constraint propagation. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 738–743. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Barnier, N., Brisset, P.: Solving kirkman’s schoolgirl problem in a few seconds. Constraints 10, 7–21 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ramani, A., Markov, I.: Automatically exploiting symmetries in constraint programming. In: Faltings, B.V., Petcu, A., Fages, F., Rossi, F. (eds.) CSCLP 2004. LNCS (LNAI), vol. 3419, pp. 98–112. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Prestwich, S.D., Roli, A.: Symmetry breaking and local search spaces. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 273–287. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Mancini, T., Cadoli, M.: Detecting and breaking symmetries by reasoning on problem specifications. In: Zucker, J.-D., Saitta, L. (eds.) SARA 2005. LNCS (LNAI), vol. 3607, pp. 165–181. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Sellmann, M., Hentenryck, P.V.: Structural symmetry breaking. In: Kaelbling, L.P., Saffiotti, A. (eds.) Nineteenth International Joint Conference on Artificial Intelligence (IJCAI-05), Edinburgh, Scotland, pp. 298–303. Professional Book Center (2005)Google Scholar
  9. 9.
    Harvey, W., Winterer, T.: Solving the MOLR and social golfers problems. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 286–300. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Gent, I., Lynce, I.: A SAT encoding for the social golfer problem. In: IJCAI 2005 workshop on Modelling and Solving Problems with Constraints, Edinburgh, Scotland (2005)Google Scholar
  11. 11.
    Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Global constraints for lexicographic orderings. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 93–108. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Dotú, I., Hentenryck, P.V.: Scheduling social golfers locally. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 155–167. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Gent, I., Walsh, T.: CSPLIB: A benchmark library for constraints. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 480–481. Springer, Heidelberg (1999)Google Scholar
  14. 14.
    Fogel, L., Owens, A., Walsh, M.: Artificial Intelligence Through Simulated Evolution. Wiley, New York (1966)zbMATHGoogle Scholar
  15. 15.
    Hinton, G., Nolan, S.: How learning can guide evolution. Complex Systems 1, 495 (1987)zbMATHGoogle Scholar
  16. 16.
    Whitley, D., Gordon, S., Mathias, K.: Lamarckian evolution, the baldwin effect and function optimization. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, Springer, Heidelberg (1994)Google Scholar
  17. 17.
    Sellmann, M.: The social golfer problem, Web site available at:

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Carlos Cotta
    • 1
  • Iván Dotú
    • 2
  • Antonio J. Fernández
    • 1
  • Pascal Van Hentenryck
    • 3
  1. 1.Dpto. de Lenguajes y Ciencias de la ComputaciónUniversidad de MálagaSpain
  2. 2.Dpto. de Ingeniería InformáticaUniversidad Autónoma de MadridSpain
  3. 3.Brown UniversityProvidenceUSA

Personalised recommendations