Constraint Satisfaction

  • Eugene C. Freuder
  • Mark Wallace
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 57)


Many problems can be formulated in terms of satisfying a set of constraints. This chapter focuses on methods for modeling and solving such problems used in artificial intelligence and implemented in constraint programming languages.


Constraint satisfaction Constraint programming Optimization CSP 


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  1. [1]
    J. Amilhastre, H. Fargier and P. Marquis (2002) Consistency restoration and explanations in dynamic CSPs—application to configuration. Artificial Intelligence, 135, 199–234.CrossRefMathSciNetGoogle Scholar
  2. [2]
    F. Bacchus, X. Chen, P. van Beek and T. Walsh (2002) Binary vs. non-binary constraints. Artificial Intelligence.Google Scholar
  3. [3]
    B. De Backer, V. Furnon, P. Prosser, P. Kilby and P. Shaw (1997) Local search in constraint programming: Application to the vehicle routing problem. Presented at the CP-97 Workshop on Industrial Constraint-based Scheduling.Google Scholar
  4. [4]
    C. Bessiere, E. Freuder and J. Regin (1999) Using constraint metaknowledge to reduce arc consistency computation, Artificial Intelligence, 107, 125–148.CrossRefMathSciNetGoogle Scholar
  5. [5]
    S. Bistarelli, H. Fargier, U. Montanari, F. Rossi, T. Schiex, and G. Verfaille (1996) Semiring-based CSPs and valued CSPs: Basic properties. In: M. Jampel, E.C. Freuder and M. Maher (eds.), Over-Constrained Systems, Volume 1106 of Lecture Notes in Computer Science. Springer, Berlin, pp. 111–150.Google Scholar
  6. [6]
    B. Cheng, K. Choi, J. Lee and J. Wu (1999) Increasing constraint propagation by redundant modeling: an experience report. Constraints, 4, 167–192.CrossRefGoogle Scholar
  7. [7]
    P. Cheeseman, B. Kanefsky and W. Taylor (1991) Where the really hard problems are. In: Proceedings Twelth International Joint Conference in Artificial Intelligence. Morgan Kaufmann, San Mateo, pp. 331–337.Google Scholar
  8. [8]
    R. Debruyne and C. Bessière (2001) Domain filtering consistencies. Journal of Artificial Intelligence Research, 14, 205–230.MathSciNetGoogle Scholar
  9. [9]
    R. Dechter (1990). Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition. Artificial Intelligence, 41, 273–312.CrossRefMathSciNetGoogle Scholar
  10. [10]
    R. Dechter and D. Frost (2002) Backjump-based backtracking for constraint satisfaction problems. Artificial Intelligence, 136, 147–188.CrossRefMathSciNetGoogle Scholar
  11. [11]
    P. Deransart, M. Hermenegildo and J. Maluszynski (eds.) (2000) Analysis and Visualization Tools for Constraint Programming. Lecture Notes in Computer Science No. 1870. Springer, Berlin.Google Scholar
  12. [12]
    R. Dechter, I. Meiri and J. Pearl (1991) Temporal constraint networks. Artificial Intelligence, 49, 61–95.CrossRefMathSciNetGoogle Scholar
  13. [13]
    E. Freuder (1978) Synthesizing constraint expressions. Communications of the ACM, 11, 958–966.MathSciNetGoogle Scholar
  14. [14]
    E. Freuder (1982) A sufficient condition for backtrack-free search. Journal of the Association for Computing Machinery, 29, 24–32.zbMATHMathSciNetGoogle Scholar
  15. [15]
    E. Freuder (1991) Eliminating interchangeable values in constraint satisfaction problems. In: Proceedings Ninth National Conference on Artificial Intelligence. AAAI Press/MIT, Menlo Park/Cambridge, pp. 227–233.Google Scholar
  16. [16]
    E. Freuder and R. Wallace (1992). Partial constraint satisfaction. Artificial Intelligence, 58, 1–70.MathSciNetGoogle Scholar
  17. [17]
    F. Focacci, A. Lodi and M. Milano (1999) Cost-based domain filtering. In: J. Jaffar (ed.), Principles and Practice of Constraint Programming Volume 1713 of Lecture Notes in Computer Science. Springer.Google Scholar
  18. [18]
    C. Gomes, B. Selman and N. Crato (1997) Heavy-tailed Distributions in Combinatorial Search. Volume 1330 of Lecture Notes in Computer Science. Springer.Google Scholar
  19. [19]
    W. Harvey and M. Ginsberg (1995) Limited discrepancy search. In: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI-95). Morgan Kaufmann, pp. 607–615.Google Scholar
  20. [20]
    P. Jeavons, D. Cohen and M. Gyssens (1997) Closure properties of constraints. Journal of the ACM, 44, 527–548.CrossRefMathSciNetGoogle Scholar
  21. [21]
    J. Jaffar and J.-L. Lassez (1987) Constraint logic programming. Proceedings of the Annual ACM Symposium on Principles of Programming Languages (POPL). ACM, pp. 111–119.Google Scholar
  22. [22]
    G. Kondrak and P. van Beek (1997) A theoretical evaluation of selected backtracking algorithms. Artificial Intelligence, 89, 365–387.CrossRefMathSciNetGoogle Scholar
  23. [23]
    F. Laburthe and Y. Caseau (1998) SALSA: a language for search algorithms. 4th International Conference on the Principles and Practice of Constraint Programming (CP’98). Pisa, Italy, October.Google Scholar
  24. [24]
    A. Mackworth (1977) Consistency in networks of relations. Artificial Intelligence, 8, 99–118.CrossRefzbMATHGoogle Scholar
  25. [25]
    S. Minton (1996) Automatically configuring constraint satisfaction programs. A case study. Constraints, 1, 7–43.CrossRefMathSciNetGoogle Scholar
  26. [26]
    S. Minton, M.D. Johnston, A.B. Philips and P. Laird (1992) Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling. Artificial Intelligence, 58, 61–205.CrossRefMathSciNetGoogle Scholar
  27. [27]
    L. Michel and P. Van Hentenryck (1999) Localizer: a modeling language for local search. INFORMS. Journal on Computing.Google Scholar
  28. [28]
    G. Pesant and M. Gendreau (1996) A view of local search in constraint programming. In: Principles and Practice of Constraint Programming CP96: Proceedings of the Second International Conference, Volume 1118 of Lecture Notes in Computer Science. Springer, Berlin, pp. 353–366.Google Scholar
  29. [29]
    J.-C. Régin (2001) Minimization of the number of breaks in sports scheduling problems using constraint programming. In: E. Freuder and R. Wallace (eds.), Constraint Programming and Large Scale Discrete Optimization, volume 57 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, Providence, RI, pp. 115–130.Google Scholar
  30. [30]
    D. Sabin and E. Freuder (1997) Understanding and Improving the MAC Algorithm. In: Principles and Practice of Constraint Programming—CP97: Proceedings of the Third International Conference, volume 1330 of Lecture Notes in Computer Science. Springer, Berlin, pp. 167–181.Google Scholar
  31. [31]
    H.M. Salkin (1970) On the merit of the generalized origin and restarts in implicit enumeration. Operations Research, 18, 549–554.zbMATHGoogle Scholar
  32. [32]
    P. Shaw (1998) Using constraint programming and local search methods to solve vehicle routing problems. In: Michael Maher and Jean Francois Puget (eds.), Principles and Practice of Constraint Programming CP98, Volume 1520 of Lecture Notes in Computer Science. Springer. pp. 417–431.Google Scholar
  33. [33]
    B. Selman, H. Levesque and D. Mitchell (1992) A new method for solving hard satisfiability problems. Proceedings of the 10th National Conference on Artificial Intelligence (AAAI-92). San Jose, CA, USA, pp. 440–446.Google Scholar
  34. [34]
    E. Tsang (1993) Foundations of Constraint Satisfaction. Academic Press, London.Google Scholar
  35. [35]
    Pascal Van Hentenryck (1999) The OPL Optimization Programming Language. The MIT Press, Cambridge, MA.Google Scholar
  36. [36]
    P. Van Hentenryck, H. Simonis and M. Dincbas (1992) Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58, 113–159.MathSciNetGoogle Scholar
  37. [37]
    G. Verfaillie, M. Lemaitre and T. Schiex (1996) Russian doll search for solving constraint optimization problems. Proceedings of AAAI, pp. 181–187.Google Scholar
  38. [38]
    A. Veron, K. Schuerman and M. Reeve (1993) Why and how in the ElipSys OR-parallel CLP system. Proceedings of PARLE.Google Scholar
  39. [39]
    M. Wallace, S. Novello and J. Schimpf (1997) ECLiPSe—a platform for constraint programming. ICL Systems Journal 12(1), 159–200.Google Scholar
  40. [40]
    T. Walsh (2002) Stochastic constraint programming. Proceedings of ECAI-2002.Google Scholar
  41. [41]
    M. Yokoo (1994) Weak-commitment search for solving constraint satisfaction problems. Proceedings of AAAI, pp. 313–318.Google Scholar
  42. [42]
    M. Yokoo, E. Durfee, T. Ishida and K. Kuwabara (1998) The distributed CSP: Formalization and algorithms. IEEE Transactions on Knowledge and Data Engineering, 10, 673–685.CrossRefGoogle Scholar
  43. [43]
    W. Zhang (1998) Complete anytime beam search. Proceedings of AAAI, pp. 425–430.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Eugene C. Freuder
    • 1
  • Mark Wallace
    • 1
  1. 1.University College Cork and Imperial CollegeUSA

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