Abstract
Over the years, a steadily improving series of local search solvers for propositional satisfiability (SAT) have been constructed. However, these solvers are often fragile, in that they have apparently minor details in their implementation that dramatically affect performance and confound understanding. In order to understand and predict the success of differing strategies, various local search metrics have been proposed. Many of these metrics summarize properties of the boolean assignments examined during the search. This has two consequences: first, they only capture one side of satisfiability, failing to characterize the behaviour with respect to constraints. Secondly, the boolean requirement limits the applicability of these metrics to more general constraint satisfaction problems (CSPs), which can have non-boolean domains.
In response, we present dual metrics, derived from existing primal (boolean assignment) metrics, that are based on the states of constraints during the search. Experimental results show a strong relationship between the primal and dual versions of these metrics on a variety of random and structured problems. This dual perspective can be easily applied to both SAT and general CSPs, allowing for new insights into the workings of a broad class of local search methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Battiti, R.: Reactive search: Toward self–tuning heuristics. In: Rayward-Smith, V.J., Osman, I.H., Reeves, C.R., Smith, G.D. (eds.) Modern Heuristic Search Methods, pp. 61–83. John Wiley & Sons Ltd., Chichester (1996)
Cha, B., Iwama, K.: Performance Test of Local Search Algorithms Using New Types of Random CNF Formulas. In: Proceedings of 14th International Joint Conference on Artificial Intelligence (IJCAI 1995), pp. 304–311. Kyushu University (1995)
Cha, B., Iwama, K.: Adding New Clauses for Faster Local Search. In: Proceedings of the 13th National Conference on Artificial Intelligence (AAAI 1996), pp. 332–337 (1996)
Frances, M., Litman, A.: On Covering Problems of Codes. Theory of Computing Systems 30, 113–119 (1997)
Gent, I.P., Walsh, T.: Towards an Understanding of Hill-Climbing Procedures for SAT. In: Proceedings of the 10th National Conference on Artificial Intelligence (AAAI 1993), pp. 28–33 (1993)
Hoos, H.: On the Run-time Behaviour of Stochastic Local Search Algorithms for SAT. In: Proceedings of the 16th National Conference on Artificial Intelligence (AAAI 1999), pp. 661–666. MIT Press, Cambridge (1999)
Hoos, H.H., Stützle, T.: SATLIB: An Online Resource for Research on SAT. In: Gent, I.P., von Maaren, H., Walsh, T. (eds.) Proceedings of the 3rd International Symposium on the Theory and Applications of Satisfiability Testing (SAT 2000), pp. 283–292. IOS Press, Amsterdam (2000)
Horvitz, E., Ruan, Y., Gomes, C.P., Kautz, H., Selman, B., Chickering, D.M.: A Bayesian approach to tackling hard computational problems. In: Proceedings of the 17th Conference on Uncertainty and Artificial Intelligence (UAI 2001), August 2001, pp. 235–244 (2001)
Hutter, F., Tompkins, D.A.D., Hoos, H.H.: Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, p. 233. Springer, Heidelberg (2002)
McAllester, D., Selman, B., Kautz, H.: Evidence for Invariants in Local Search. In: Proceedings of the 14th National Conference on Artificial Intelligence (AAAI 1997). AT&T Laboratories (1997)
Schuurmans, D., Southey, F.: Local search characteristics of incomplete SAT procedures. Artificial Intelligence 132(2), 121–150 (2001)
Schuurmans, D., Southey, F., Holte, R.C.: The exponentiated subgradient algorithm for heuristic boolean programming. In: Proceedings of 17th International Joint Conference on Artificial Intelligence (IJCAI 2001), vol. 1, pp. 334–341 (2001)
Selman, B., Kautz, H.A., Cohen, B.: Noise Strategies for Improving Local Search. In: Proceedings of the 12th National Conference on Artificial Intelligence (AAAI 1994), July 1994, AT&T Bell Labs (1994)
Selman, B., Levesque, H., Mitchell, D.: A New Method for Solving Hard Satisfiability Problems. In: Proceedings of the 10th National Conference on Artificial Intelligence (AAAI 1992), AT&T, University of Toronto, Simon Fraser, pp. 440–446 (1992)
Thornton, J.R., Pham, D.N., Bain, S., Ferreira Jr., V.: Additive versus Multiplicative Clause Weighting for SAT. In: Proceedings of the 19th National Conference on Artificial Intelligence (AAAI 2004) (2004)
Wu, Z., Wah, B.W.: Solving Hard Satisfiability Problems: A Unified Algorithm Based On Discrete Lagrange Multipliers. In: Proceedings of 11th IEEE Conference on Tools with Artificial Intelligence. UIUC (November 1999)
Wu, Z., Wah, B.W.: Trap Escaping Strategies in Discrete Lagrangian Methods for Solving Hard Satisfiability and Maximum Satisfiability Problems. In: Proceedings of the 16th National Conference on Artificial Intelligence (AAAI 1999) (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Southey, F. (2005). Constraint Metrics for Local Search. In: Bacchus, F., Walsh, T. (eds) Theory and Applications of Satisfiability Testing. SAT 2005. Lecture Notes in Computer Science, vol 3569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499107_20
Download citation
DOI: https://doi.org/10.1007/11499107_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26276-3
Online ISBN: 978-3-540-31679-4
eBook Packages: Computer ScienceComputer Science (R0)