Abstract
Local search achieves good results on a variety of SAT problems and often scales up better than backtrack search. But despite recent advances in local search heuristics it has failed to solve some structured problems, while backtrack search has advanced greatly on such problems. We conjecture that current modelling practices are unintentionally biased in favour of solution by backtrack search. To test this conjecture we remodel two problems whose large instances have long resisted solution by local search: parity learning and Towers of Hanoi as STRIPS planning. By reducing variable dependencies and using other techniques we boost local search performance by several orders of magnitude in both cases, and we can now solve 32-bit and 6-disk instances for the first time using a standard SAT local search algorithm.
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
Ansótegui, C., Manyà, F.: Mapping Problems With Finite-Domain Variables into Problems With Boolean Variables. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 1–15. Springer, Heidelberg (2005)
Bailleux, O., Boufkhad, Y.: Efficient CNF Encoding of Boolean Cardinality Constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 108–122. Springer, Heidelberg (2003)
Baumgartner, P., Massacci, F.: The Taming of the (X)OR. In: Palamidessi, C., et al. (eds.) CL 2000. LNCS (LNAI), vol. 1861, Springer, Heidelberg (2000)
Crawford, J.M., Kearns, M.J., Shapire, R.E.: The Minimal Disagreement Parity Problem as a Hard Satisfiability Problem. Technical report, Computational Intelligence Research Laboratory and AT&T Bell Labs (1994)
Ernst, M., Millstein, T., Weld, D.S.: Automatic SAT-Compilation of Planning Problems. In: Fifteenth International Joint Conference on Artificial Intelligence, Morgan Kaufmann, San Francisco (1997)
Fikes, R.E., Nilsson, N.J.: STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving. Artificial Intelligence 2(3-4), 189–208 (1971)
Gent, I.P.: Arc Consistency in SAT. In: Fifteenth European Conference on Artificial Intelligence, pp. 121–125. IOS Press, Amsterdam (2002)
Gent, I.P., Prosser, P.: SAT Encodings of the Stable Marriage Problem With Ties and Incomplete Lists. In: Fifth International Symposium on Theory and Applications of Satisfiability Testing (2002)
Gent, I.P., Prosser, P., Smith, B.: A 0/1 Encoding of the GACLex Constraint for Pairs of Vectors. In: International Workshop on Modelling and Solving Problems With Constraints, ECAI (2002)
Haas, A.: The Case for Domain-Specific Frame Axioms. In: Brown, F.M. (ed.) The Frame Problem in Artificial Intelligence: Proceedings of the 1987 Workshop, Morgan Kaufmann, San Francisco (1987)
Hirsch, E.A., Kojevnikov, A.: Solving Boolean Satisfiability Using Local Search Guided by Unit Clause Elimination. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 605–609. Springer, Heidelberg (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, pp. 233–248. Springer, Heidelberg (2002)
Kasif, S.: On the Parallel Complexity of Discrete Relaxation in Constraint Satisfaction Networks. Artificial Intelligence 45, 275–286 (1990)
Kautz, H., McAllester, D., Selman, B.: Encoding Plans in Propositional Logic. In: Fifth International Conference on Principles of Knowledge Representation and Reasoning (1996)
Kautz, H., McAllester, D., Selman, B.: Exploiting Variable Dependency in Local Search. In: Poster Sessions of the Fifteenth International Joint Conference on Artificial Intelligence (1997)
Kautz, H., Selman, B.: Ten Challenges Redux: Recent Progress in Propositional Reasoning and Search. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 1–18. Springer, Heidelberg (2003)
Kautz, H., Selman, B.: Planning as Satisfiability. In: Tenth European Conference on Artificial Intelligence, pp. 359–363. Wiley, Chichester (1992)
Kautz, H., Selman, B.: Pushing the Envelope: Planning, Propositional Logic and Stochastic Search. In: National Conference on Artificial Intelligence, pp. 1194–1201. AAAI Press, Menlo Park (1996)
Li, C.: Integrating Equivalence Reasoning into Davis-Putnam Procedure. In: Seventeenth National Conference on Artificial Intelligence, pp. 291–296. AAAI Press, Menlo Park (2000)
Massacci, F.: Using Walk-SAT and Rel-SAT for Cryptographic Key Search. In: International Joint Conference on Artificial Intelligence, pp. 290–295 (1999)
Minton, S., et al.: Minimizing Conflicts: a Heuristic Repair Method for Constraint Satisfaction and Scheduling Problems. Artificial Intelligence 58(1-3), 161–205 (1992)
Muhammad, R., Stuckey, P.J.: A Stochastic Non-CNF SAT Solver. In: Yang, Q., Webb, G. (eds.) PRICAI 2006. LNCS (LNAI), vol. 4099, pp. 120–129. Springer, Heidelberg (2006)
Pham, D.N., Thornton, J.R., Sattar, A.: Building Structure into Local Search for SAT. In: Twentieth International Joint Conference on Artificial Intelligence, Hyderabad, India, pp. 2359–2364 (2007)
Prestwich, S.D.: SAT Problems With Chains of Dependent Variables. Discrete Applied Mathematics 3037, 1–22 (2002)
Prestwich, S.D.: Negative Effects of Modeling Techniques on Search Performance. Annals of Operations Research 118, 137–150 (2003)
Prestwich, S.D.: Modelling Clique Problems for SAT Local Search. In: Third International Workshop on Local Search Techniques in Constraint Satisfaction (to appear) (2006)
Prestwich, S.D., Roli, A.: Symmetry Breaking and Local Search Spaces. In: Barták, R., Milano, M. (eds.) CPAIOR 2005. LNCS, vol. 3524, pp. 273–287. Springer, Heidelberg (2005)
Selman, B.: Personal communication
Selman, B., Kautz, H.A., McAllester, D.A.: Ten Challenges in Propositional Reasoning and Search. In: Fifteenth International Joint Conference on Artificial Intelligence, pp. 50–54. Morgan Kaufmann, San Francisco (1997)
Tompkins, D.A.D., Hoos, H.H.: UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT and MAX-SAT. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 306–320. Springer, Heidelberg (2005)
Warners, J.P.: A Linear-Time Transformation of Linear Inequalities Into Conjunctive Normal Form. Information Processing Letters 68, 63–69 (1998)
Warners, J., van Maaren, H.: A Two Phase Algorithm for Solving a Class of Hard Satisfiability Problems. Operations Research Letters 23(3–5), 81–88 (1999)
Wei, W., Selman, B.: Accelerating Random Walks. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 216–232. Springer, Heidelberg (2002)
Wu, Z., Wah, B.: An Efficient Global-Search Strategy in Discrete Lagrangian Methods for Solving Hard Satisfiability Problems. In: Seventeenth National Conference on Artificial Intelligence, pp. 310–315 (2000)
Zarpas, E.: Back to the SAT05 Competition: an a Posteriori Analysis of Solver Performance on Industrial Benchmarks. Journal on Satisfiability, Boolean Modeling and Computation (research note) 2, 229–237 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Prestwich, S. (2007). Variable Dependency in Local Search: Prevention Is Better Than Cure. In: Marques-Silva, J., Sakallah, K.A. (eds) Theory and Applications of Satisfiability Testing – SAT 2007. SAT 2007. Lecture Notes in Computer Science, vol 4501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72788-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-72788-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72787-3
Online ISBN: 978-3-540-72788-0
eBook Packages: Computer ScienceComputer Science (R0)