Abstract
It has been widely observed that there is no “dominant” SAT solver; instead, different solvers perform best on different instances. Rather than following the traditional approach of choosing the best solver for a given class of instances, we advocate making this decision online on a per-instance basis. Building on previous work, we describe a per-instance solver portfolio for SAT, SATzilla-07, which uses so-called empirical hardness models to choose among its constituent solvers. We leverage new model-building techniques such as censored sampling and hierarchical hardness models, and demonstrate the effectiveness of our techniques by building a portfolio of state-of-the-art SAT solvers and evaluating it on several widely-studied SAT data sets. Overall, we show that our portfolio significantly outperforms its constituent algorithms on every data set. Our approach has also proven itself to be effective in practice: in the 2007 SAT competition, SATzilla-07 won three gold medals, one silver, and one bronze; it is available online at http://www.cs.ubc.ca/labs/beta/Projects/SATzilla .
This is a preview of subscription content, log in via an institution to check access.
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
Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 341–355. Springer, Heidelberg (2004)
Bertsekas, D.P.: Linear Network Optimization, Algorithms and Codes. MIT Press, Cambridge, MA (1991)
Carchrae, T., Beck, J.C.: Applying machine learning to low-knowledge control of optimization algorithms. Computational Intelligence 21(4), 372–387 (2005)
Dubois, O., Dequen, G.: A backbone-search heuristic for efficient solving of hard 3-SAT formulae. In: IJCAI 2001, pp. 248–253 (2001)
Eén, N., Sörensson, N.: An extensible SAT solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Eén, N., Sörensson, N.: Minisat v2.0 (beta). Solver description, SAT Race (2006)
Gagliolo, M., Schmidhuber, J.: Learning dynamic algorithm portfolios. Annals of Mathematics and Artificial Intelligence 47(3-4), 295–328 (2007)
Gebruers, C., Hnich, B., Bridge, D., Freuder, E.: Using CBR to select solution strategies in constraint programming. In: Muñoz-Ávila, H., Ricci, F. (eds.) ICCBR 2005. LNCS (LNAI), vol. 3620, pp. 222–236. Springer, Heidelberg (2005)
Gomes, C.P., Selman, B.: Problem structure in the presence of perturbations. In: AAAI 1997, pp. 221–226 (1997)
Gomes, C.P., Selman, B.: Algorithm portfolios. Artificial Intelligence 126(1-2), 43–62 (2001)
Heule, M., Maaren, H.V.: march_dl: Adding adaptive heuristics and a new branching strategy. Journal on Satisfiability, Boolean Modeling and Computation 2, 47–59 (2006)
Horvitz, E., Ruan, Y., Gomes, C.P., Kautz, H., Selman, B., Chickering, D.M.: A Bayesian approach to tackling hard computational problems. In: Proc. of UAI 2001, pp. 235–244 (2001)
Hutter, F., Hamadi, Y., Hoos, H.H., Leyton-Brown, K.: Performance prediction and automated tuning of randomized and parametric algorithms. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 213–228. Springer, Heidelberg (2006)
Krishnapuram, B., Carin, L., Figueiredo, M., Hartemink, A.: Sparse multinomial logistic regression: Fast algorithms and generalization bounds. IEEE Transactions on Pattern Analysis and Machine Intelligence, 957–968 (2005)
Kullmann, O.: Investigating the behaviour of a SAT solver on random formulas (2002), http://cs-svr1.swan.ac.uk/~csoliver/Artikel/OKsolverAnalyse.html
Lagoudakis, M.G., Littman, M.L.: Learning to select branching rules in the DPLL procedure for satisfiability. In: LICS/SAT, vol. 9, pp. 344–359 (2001)
Leyton-Brown, K., Nudelman, E., Andrew, G., McFadden, J., Shoham, Y.: Boosting as a metaphor for algorithm design. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 899–903. Springer, Heidelberg (2003)
Leyton-Brown, K., Nudelman, E., Andrew, G., McFadden, J., Shoham, Y.: A portfolio approach to algorithm selection. In: IJCAI 2003, pp. 1542–1543 (2003)
Leyton-Brown, K., Nudelman, E., Shoham, Y.: Learning the empirical hardness of optimization problems: The case of combinatorial auctions. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 556–572. Springer, Heidelberg (2002)
Lobjois, L., Lemaître, M.: Branch and bound algorithm selection by performance prediction. In: AAAI 1998, pp. 353–358 (1998)
Schmidhuber, J., Gagliolo, M.: Impact of censored sampling on the performance of restart strategies. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 167–181. Springer, Heidelberg (2006)
Mahajan, Y.S., Fu, Z., Malik, S.: Zchaff2004: an efficient SAT solver. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 360–375. Springer, Heidelberg (2005)
Nadel, A., Gordon, M., Palti, A., Hanna, Z.: Eureka-2006 SAT solver. Solver description, SAT Race (2006)
Nudelman, E., Leyton-Brown, K., Hoos, H.H., Devkar, A., Shoham, Y.: Understanding random SAT: Beyond the clauses-to-variables ratio. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 438–452. Springer, Heidelberg (2004)
Pipatsrisawat, K., Darwiche, A.: Rsat 1.03: SAT solver description. Technical Report D-152, Automated Reasoning Group, UCLA (2006)
Rice, J.R.: The algorithm selection problem. Advances in Computers 15, 65–118 (1976)
Schmee, J., Hahn, G.J.: A simple method for regression analysis with censored data. Technometrics 21(4), 417–432 (1979)
Vallstrom, D.: Vallst documentation (2005), http://vallst.satcompetition.org/index.html
Xu, L., Hoos, H.H., Leyton-Brown, K.: Hierarchical hardness models for SAT. In: CP 2007 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K. (2007). SATzilla-07: The Design and Analysis of an Algorithm Portfolio for SAT. In: Bessière, C. (eds) Principles and Practice of Constraint Programming – CP 2007. CP 2007. Lecture Notes in Computer Science, vol 4741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74970-7_50
Download citation
DOI: https://doi.org/10.1007/978-3-540-74970-7_50
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74969-1
Online ISBN: 978-3-540-74970-7
eBook Packages: Computer ScienceComputer Science (R0)