Abstract
Stochastic local search solvers for SAT made a large progress with the introduction of probability distributions like the ones used by the SAT Competition 2011 winners Sparrow2010 and EagleUp. These solvers though used a relatively complex decision heuristic, where probability distributions played a marginal role.
In this paper we analyze a pure and simple probability distribution based solver probSAT, which is probably one of the simplest SLS solvers ever presented. We analyze different functions for the probability distribution for selecting the next flip variable with respect to the performance of the solver. Further we also analyze the role of make and break within the definition of these probability distributions and show that the general definition of the score improvement by flipping a variable, as make minus break is questionable. By empirical evaluations we show that the performance of our new algorithm exceeds that of the SAT Competition winners by orders of magnitude.
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References
Balint, A., Diepold, D., Gall, D., Gerber, S., Kapler, G., Retz, R.: EDACC - An Advanced Platform for the Experiment Design, Administration and Analysis of Empirical Algorithms. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 586–599. Springer, Heidelberg (2011)
Balint, A., Fröhlich, A.: Improving Stochastic Local Search for SAT with a New Probability Distribution. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 10–15. Springer, Heidelberg (2010)
Biere, A.: Lingeling and Friends at the SAT Competition 2011. Tehnical report 11/1, FMV Reports Series (2011), http://fmv.jku.at/papers/Biere-FMV-TR-11-1.pdf
bwGRiD, member of the German D-Grid initiative, funded by the Ministry for Education and Research (Bundesministerium für Bildung und Forschung) and the Ministry for Science, Research and Arts Baden-Württemberg (Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg), http://www.bw-grid.de
Birattari, M., Yuan, Z., Balaprakash, P., Stützle, T.: F-Race and Iterated F-Race: An Overview. In: Bartz-Beielstein, T., et al. (eds.) Empirical Methods for the Analysis of Optimization Algorithms, pp. 311–336. Springer, Berlin (2010)
Hoos, H.H.: An adaptive noise mechanism for WalkSAT. In: Proceedings of AAAI 2002, pp. 635–660 (2002)
Kroc, L., Sabharwal, A., Selman, B.: An Empirical Study of Optimal Noise and Runtime Distributions in Local Search. In: Strichman, O., Szeider, S. (eds.) SAT 2010. LNCS, vol. 6175, pp. 346–351. Springer, Heidelberg (2010)
Li, C.-M., Huang, W.Q.: Diversification and Determinism in Local Search for Satisfiability. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 158–172. Springer, Heidelberg (2005)
Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. Information Proc. Letters 47, 173–180 (1993)
McAllester, D., Selman, B., Kautz, H.: Evidence for invariant in local search. In: Proceedings of AAAI 1997, pp. 321–326 (1997)
Papadimitriou, C.H.: On selecting a satisfying truth assignment. In: Proceedings FOCS 1991, pp. 163–169. IEEE (1991)
Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: Proceedings FOCS 1991, pp. 410–414. IEEE (1999)
Schöning, U.: Principles of Stochastic Local Search. In: Akl, S.G., Calude, C.S., Dinneen, M.J., Rozenberg, G., Wareham, H.T. (eds.) UC 2007. LNCS, vol. 4618, pp. 178–187. Springer, Heidelberg (2007)
Seitz, S., Alava, M., Orponen, P.: Focused local search for random 3-satisfiability. arXiv:cond-mat/051707v1 (2005)
Tompkins, D.A.D., Balint, A., Hoos, H.H.: Captain Jack: New Variable Selection Heuristics in Local Search for SAT. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 302–316. Springer, Heidelberg (2011)
The SAT Competition Homepage, http://www.satcompetition.org
Braunstein, A., Mezard, M., Zecchina, R.: Survey propagation: an algorithm for satisfiability. Random Structures and Algorithms 27, 201–226 (2005)
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Balint, A., Schöning, U. (2012). Choosing Probability Distributions for Stochastic Local Search and the Role of Make versus Break. In: Cimatti, A., Sebastiani, R. (eds) Theory and Applications of Satisfiability Testing – SAT 2012. SAT 2012. Lecture Notes in Computer Science, vol 7317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31612-8_3
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DOI: https://doi.org/10.1007/978-3-642-31612-8_3
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