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Abstract

The scheduling of social golfers has attracted significant attention in recent years because of its highly symmetrical and combinatorial nature. In particular, it has become one of the standard benchmarks for symmetry breaking in constraint programming. This paper presents a very effective, local search, algorithm for scheduling social golfers. The algorithm find the first known solutions to 11 instances and matches, or improves, state-of-the-art results from constraint programming on all but 3 instances. Moreover, most instances of the social golfers are solved within a couple of seconds. Interestingly, the algorithm does not incorporate any symmetry-breaking scheme and illustrates the nice complementarity between constraint programming and local search on this scheduling application.

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References

  1. 1.
    Ågren, M.: Solving the Social Golfer Using Local Search (2003), http://peg.it.uu.se/~saps02/MagnusAgren/
  2. 2.
    Barnier, N., Brisset, P.: Solving kirkman’s schoolgirl problem in a few seconds. Constraints (2005); Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, p. 477. Springer, Heidelberg (2002)Google Scholar
  3. 3.
    Colbourn, C., Dinitz, J.H.: The CRC Handbook of Combinatorial Design. CRC Press, Boca Raton (1996)CrossRefGoogle Scholar
  4. 4.
    Colbourn, C.J., Dinitz, J.H.: Mutually orthogonal latin squares: A brief survey of constructions. Journal of Statistical Planning and Inference 95, 9–48 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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
  6. 6.
    Prestwich, S.: Randomized backtracing for linear pseudo-boolean constraint problems. In: Proceedings of the Fourth International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CP-AI-OR 2002), Le Croisic, France, March 2002, pp. 7–19 (2002)Google Scholar
  7. 7.
    Prestwich, S.D.: Supersymmetric Modeling for Local Search. In: Second International Workshop on Symmetry in Constraint Satisfaction Problems (2002)Google Scholar
  8. 8.
    Prestwich, S.D.: Negative Effects of Modeling Techniques on Search Performance. Annals of Operations Research 118, 137–150 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Puget, J.F.: Symmetry breaking revisited. Constraints (2005); Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, p. 446. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Sellmann, M.: Reduction Techniques in Constraint Programming and Combinatorial Optimization. PhD thesis, University of Paderborn, Germany (2003)Google Scholar
  11. 11.
    Sellmann, M., Harvey, W.: Heuristic constraint propagation – Using local search for incomplete pruning and domain filtering of redundant constraints for the social golfer problem. In: Jussien, N., Laburthe, F. (eds.) Proceedings of the Fourth International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CP-AI-OR 2002), Le Croisic, France, March 2002, pp. 191–204 (2002)Google Scholar
  12. 12.
    Smith, B.: Reducing Symmetry in a Combinatorial Design Problem. In: CP-AI-OR 2001, Wye College (Imperial College), Ashford, Kent UK, April 2001, pp. 351–359 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Iván Dotú
    • 1
  • Pascal Van Hentenryck
    • 2
  1. 1.Departamento De Ingeniería InformáticaUniversidad Autónoma de Madrid 
  2. 2.Brown UniversityProvidenceUSA

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