Scaling and Probabilistic Smoothing: Dynamic Local Search for Unweighted MAX-SAT
In this paper, we study the behaviour of the Scaling and Probabilistic Smoothing (SAPS) dynamic local search algorithm on the unweighted MAX-SAT problem. MAX-SAT is a conceptually simple combinatorial problem of substantial theoretical and practical interest; many application-relevant problems, including scheduling problems or most probable explanation finding in Bayes nets, can be encoded and solved as MAX-SAT. This paper is a natural extension of our previous work, where we introduced SAPS, and demonstrated that it is amongst the state-of-the-art local search algorithms for solvable SAT problem instances. We present results showing that SAPS is also very e.ective at finding optimal solutions for unsatisfiable MAX-SAT instances, and in many cases performs better than state-of-the-art MAX-SAT algorithms, such as the Guided Local Search algorithm by Mills and Tsang . With the exception of some configuration parameters, we found that SAPS did not require any changes to effeciently solve unweighted MAX-SAT instances. For solving weighted MAX-SAT instances, a modified SAPS algorithm will be necessary, and we provide some thoughts on this topic of future research.
Unable to display preview. Download preview PDF.
- P. Cheeseman, B. Kanefsky and W. M. Taylor. Where the Really Hard Problems Are. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, IJCAI-91,.331–337, 1997.Google Scholar
- J. Frank. Learning Short-term Clause Weights for GSAT. In Proc. IJCAI-97, pp. 384–389, Morgan Kaufmann Publishers, 1997.Google Scholar
- H. H. Hoos. On the Run-time Behaviour of Stochastic Local Search Algorithms for SAT. In Proc. AAAI-99, pp 661–666. AAAI Press, 1999.Google Scholar
- F. Hutter, D. A. D. Tompkins, and H. H. Hoos. Scaling and Probabilistic Smoothing: Effecient Dynamic Local Search for SAT. In LNCS 2470:Proc. CP-02, pp 233–248, Springer Verlag, 2002.Google Scholar
- P. Morris. The breakout method for escaping from local minima. In Proc. AAAI-93, pp 40–45. AAAI Press, 1993.Google Scholar
- J. D. Park. Using Weighted MAX-SAT Engines to Solve MPE. In Proc. AAAI-02, pp 682–687. AAAI Press, 2002.Google Scholar
- D. Schuurmans and F. Southey. Local search characteristics of incomplete SAT procedures. In Proc. AAAI-2000, pp 297–302, AAAI Press, 2000. Scaling and Probabilistic Smoothing: Dynamic Local SearchGoogle Scholar
- D. Schuurmans, F. Southey, and R.C. Holte. The exponentiated subgradient algorithm for heuristic boolean programming. In Proc. IJCAI-01, pp 334–341, Morgan Kaufmann Publishers, 2001.Google Scholar
- B. Selman and H. A. Kautz. Domain-Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems. In Proc. IJCAI-93, pp 290–295, Morgan Kaufmann Publishers, 1993.Google Scholar
- B. Selman, H.A. Kautz, and B. Cohen. Noise Strategies for Improving Local Search. In Proc. AAAI-94, pp 337–343, AAAI Press, 1994.Google Scholar
- B. Selman, H. Levesque, and D. Mitchell. A New Method for Solving Hard Satisfiability Problems. In Proc. AAAI-92, pp 440–446, AAAI Press, 1992.Google Scholar
- K. Smyth, H. H. Hoos, and T. Stutzle. Iterated Robust Tabu Search for MAXSAT. In Proc. of the 16th Canadian Conference on Artificial Intelligence (AI 2003), to appear, 2003.Google Scholar
- Z. Wu and B. W. Wah. An Effecient Global-Search Strategy in Discrete Lagrangian Methods for Solving Hard Satisfiability Problems. In Proc. AAAI-00, pp. 310–315, AAAI Press, 2000.Google Scholar