Abstract
Local search techniques have attracted considerable interest in the AI community since the development of GSAT for solving large propositional SAT problems. Newer SAT techniques, such as the Discrete Lagrangian Method (DLM), have further improved on GSAT and can also be applied to general constraint satisfaction and optimisation. However, little work has applied local search to MAX-SAT problems with hard and soft constraints. As many real-world problems are best represented by hard (mandatory) and soft (desirable) constraints, the development of effective local search heuristics for this domain is of significant practical importance.
This paper extends previous work on dynamic constraint weighting by introducing a two-level heuristic that switches search strategy according to whether a current solution contains unsatisfied hard constraints. Using constraint weighting techniques derived from DLM to satisfy hard constraints, we apply a Tabu search to optimise the soft constraint violations. These two heuristics are further combined with a dynamic hard constraint multiplier that changes the relative importance of the hard constraints during the search. We empirically evaluate this new algorithm using a set of randomly generated 3-SAT problems of various sizes and difficulty, and in comparison with various state-of-the-art SAT techniques. The results indicate that our dynamic, two-level heuristic offers significant performance benefits over the standard SAT approaches.
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The authors gratefully acknowledge the financial support of the Australian Research Council, grant A00000118, in the conduct of this research
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References
U. Bistarelli, S. Montanari and F. Rossi. Semiring-based constraint solving and optimization. Journal of ACM, 44(2):201–236, 1997.
A. Borning, B. Freeman-Benson, and M. Wilson. Constraint hierarchies. Lisp and Symbolic Computation, 5(3):223–270, 1992.
B. Cha, K. Iwama, Y. Kambayashi, and S. Miyazaki. Local search algorithms for partial MAX-SAT. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI-97), pages 332–337, 1997.
J. Frank. Learning short term weights for GSAT. In Proceedings of theF ourteenth National Conference on Artificial Intelligence (AAAI-97), pages 384–389, 1997.
E. Freuder and R. Wallace. Partial constraint satisfaction. Artificial Intelligence, 58(1):21–70, 1992.
F. Glover. Tabu search: Part 1. ORSA Journal on Computing, 1(3):190–206, 1989.
M. Heinz, L. Fong, L. Chong, S. Ping, J. Walser, and R. Yap. Solving hierarchical constraints over finite domains. In Proceedings of theSixth International Symposium on Artificial Intelligence and Mathematics, 2000.
H. Hoos. On the run-time behavior of stochastic local search algorithms for SAT. In Proceedings of the Sixteenth National Conference on Artificial Intelligence (AAAI-99), pages 661–666, 1999.
H. Jiang, Y. Kautz and B. Selman. Solving problems with hard and soft constraints using a stochastic algorithm for MAX-SAT. In First International Joint Workshop on Artificial Intelligence and Operations Research, 1995.
D. McAllester, B. Selman, and H. Kautz. Evidence for invariance in local search. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI-97), pages 321–326, 1997.
P. Mills and E. Tsang. Guided local search applied to the satisfiability (SAT) problem. In Proceedings of the15th National Conferenceof theA ustralian Society for Operations Research (ASOR’99), pages 872–883, 1999.
P. Mills and E. Tsang. Guided local search for solving SAT and weighted MAXSAT problems. Journal of Automated Reasoning, 24:205–223, 2000.
P. Morris. The Breakout method for escaping local minima. In Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI-93), pages 40–45, 1993.
A. Schaerf. Tabu search for large high school timetabling problems. In Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI-96), pages 363–368, 1996.
D. Schuurmans and F. Southey. Local search characteristics of incomplete SAT procedures. In Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI-00), pages 297-302, 2000.
Y. Shang and B. Wah. A discrete Lagrangian-based global search method for solving satisfiability problems. J. Global Optimization, 12:61–99, 1998.
J. Thornton, W. Pullan, and J. Terry. Towards fewer parameters for SAT clause weighting algorithms. In Proceedings of the Fifteenth Australian Joint Conference on Artificial Intelligence (AI’2002), To appear, 2002.
J. Thornton and A. Sattar. Dynamic constraint weighting for over-constrained problems. In Proceedings of the Fifth Pacific Rim Conference on Artificial Intelligence (PRICAI-98), pages 377–388, 1998.
Wu Z. TheThe ory and Applications of DiscreteConstr ained Optimization using LagrangeMultiplie rs. PhD thesis, Department of Computer Science, University of Illinois, 2000.
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Thornton, J., Bain, S., Sattar, A., Pham, D.N. (2002). A Two Level Local Search for MAX-SAT Problems with Hard and Soft Constraints. In: McKay, B., Slaney, J. (eds) AI 2002: Advances in Artificial Intelligence. AI 2002. Lecture Notes in Computer Science(), vol 2557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36187-1_53
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DOI: https://doi.org/10.1007/3-540-36187-1_53
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