A key feature of constraint programming is the ability to design specific search strategies to solve problems. On the contrary, integer programming solvers have used efficient general-purpose strategies since their earliest implementations. We present a new general purpose search strategy for constraint programming inspired from integer programming techniques and based on the concept of the impact of a variable. The impact measures the importance of a variable for the reduction of the search space. Impacts are learned from the observation of domain reduction during search and we show how restarting search can dramatically improve performance. Using impacts for solving multiknapsack, magic square, and Latin square completion problems shows that this new criteria for choosing variables and values can outperform classical general-purpose strategies.


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  1. 1.
    ILOG CPLEX 9.0. User Manual. ILOG, S.A., Gentilly, France (September 2003)Google Scholar
  2. 2.
    Benichou, M., Gauthier, J.M., Girodet, P., Hentges, G., Ribiere, G., Vincent, O.: Experiments in mixed-integer linear programming. Mathematical Programming (1), 76–94 (1971)Google Scholar
  3. 3.
    Bessiere, C., Chmeiss, A., Sais, L.: Neighborhood-based variable ordering heuristics for the constraint satisfaction problem. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 565–569. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Bessière, C., Régin, J.-C.: MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 61–75. Springer, Heidelberg (1996)Google Scholar
  5. 5.
    Bixby, R.E., Cook, W., Cox, A., Lee, E.K.: Parallel mixed integer programming. Technical Report Research Monograph CRPC-TR95554, Center for Research on Parallel Computation (1995)Google Scholar
  6. 6.
    Brélaz, D.: New methods to color the vertices of a graph. Communication of the ACM (22), 251–256 (1979)Google Scholar
  7. 7.
    Gauthier, J.-M., Ribiere, G.: Experiments in mixed-integer linear programming using pseudo-costs. Mathematical Programming (12), 26–47 (1977)Google Scholar
  8. 8.
    Gomes, C.: Complete randomized backtrack search (survey). In: Milano, M. (ed.) Constraint and Integer Programming: Toward a Unified Methodology, pp. 233–283. Kluwer, Dordrecht (2003)Google Scholar
  9. 9.
    Gomes, C., Regin, J.-C.: Modelling alldi. matrix models in constraint programming. In: Optimization days, Montreal, Canada (2003)Google Scholar
  10. 10.
    Gomes, C., Shmoys, D.: Completing quasigroups or latin squares: A structured graph coloring problem. In: Proceedings of the Computational Symposium on Graph Coloring and Extensions (2002)Google Scholar
  11. 11.
    Haralick, R., Elliot, G.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence (14), 263–313 (1980)Google Scholar
  12. 12.
    Linderoth, J., Savelsberg, M.: A computational study of search strategies for mixed integer programming. INFORMS Journal on Computing 11(2), 173–187 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    McGregor, J.J.: Relational consistency algorithms and their application in finding subgraph and graph isomorphisms. Information Science 19, 229–250 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Moskewicz, M.W., Madigan, C.F., Malik, S.: Chaff: Engineering an efficient SAT solver. In: Design Automation Conference (2001)Google Scholar
  15. 15.
    Smith, B.: The Brelaz heuristic and optimal static ordering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 405–418. Springer, Heidelberg (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Philippe Refalo
    • 1
  1. 1.ILOG, Les TaissounieresSophia AntipolisFrance

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