Heuristic methods for over-constrained constraint satisfaction problems

Constraint Satisfaction Problems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1106)


Heuristic repair methods have successfully solved constraint satisfaction problems (CSPs) and satisfiability problems (SAT) that are too large to be solved by complete algorithms. In this paper we develop methods for testing the efficiency and quality of solution returned by these methods when applied to overconstrained CSPs and SAT. The key strategy is to test heuristic methods on problems of moderate size with known optimal distances (number of constraint violations), as determined with complete algorithms. This allows us to determine whether heuristic methods find optimal distances and allows us to carry out more incisive analyses of efficiency when different strategies are incorporated into these methods and parameter values are varied. The present work tested the min-conflicts algorithm with CSPs, either alone or in combination with walk, reset or tabu strategies. SAT was tested with GSAT and walk-SAT. The best results for min-conflicts were found with the walk strategy, when the probability of random assignment was set at 0.10 or 0.15. Both GSAT and walk-SAT readily found optimal solutions for 3-SAT, the latter being somewhat faster overall.


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  1. 1.
    E. C. Freuder and R. J. Wallace. Partial constraint satisfaction. Artificial Intelligence, 58:21–70, 1992.MathSciNetGoogle Scholar
  2. 2.
    F. Glover. Tabu search: a tutorial. Interfaces, 20:74–94, 1990.Google Scholar
  3. 3.
    S. Minton, M. D. Johnston, A. B. Philips, and P. Laird. Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems. Artificial Intelligence, 58:161–205, 1992.MathSciNetGoogle Scholar
  4. 4.
    B. Selman and H. A. Kautz. An empirical study of greedy local search for satisfiability testing. In Proceedings AAAI-93, pages 46–51, 1993.Google Scholar
  5. 5.
    B. Selman, H. Levesque, and D. Mitchell. A new method for solving hard satisfiability problems. In Proceedings AAAI-92, pages 440–446, 1992.Google Scholar
  6. 6.
    R. J. Wallace and E. C. Freuder. Comparing constraint satisfaction and Davis-Putnam algorithms for the maximal satisfiability problem. In D. S. Johnson and M. A. Trick, editors, Cliques, Coloring and Satisfiability: Second DIMACS Implementation Challenge, (to appear). Amer. Math. Soc., 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.University of New HampshireDurhamUSA

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