Engineering a Lightweight and Efficient Local Search SAT Solver

  • Adrian Balint
  • Uwe SchöningEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9220)


One important category of SAT solver implementations use stochastic local search (SLS, for short). These solvers try to find a satisfying assignment for the input Boolean formula (mostly, required to be in CNF) by modifying the (mostly randomly chosen) initial assignment by bit flips until a satisfying assignment is possibly reached. Usually such SLS type algorithms proceed in a greedy fashion by increasing the number of satisfied clauses until some local optimum is reached. Trying to find its way out of such local optima typically requires the use of randomness. We present an easy, straightforward SLS type SAT solver, called probSAT, which uses just one simple strategy being based on biased probabilistic flips. Within an extensive empirical study we evaluate the current state-of-the-art solvers on a wide range of SAT problems, and show that our approach is able to exceed the performance of other solving techniques.



We would like to thank the BWGrid [8] project for providing the computational resources. This project was funded by the Deutsche Forschungsgemeinschaft (DFG) under the number SCHO 302/9-1. We thank Daniel Diepold and Simon Gerber for implementing the F-race configurator and providing different analysis tools within the EDACC framework. We would also like to thank Andreas Fröhlich for fruitful discussions on this topic and Armin Biere for helpful suggestions regarding code optimizations.


  1. 1.
    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). doi: 10.1007/978-3-642-25566-3_46 CrossRefGoogle Scholar
  2. 2.
    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). doi: 10.1007/978-3-642-14186-7_3 CrossRefGoogle Scholar
  3. 3.
    Balint, A., Manthey, N.: Analysis of preprocessing techniques and their utility for CDCL and SLS solver. In: Proceedings of POS2013 (2013)Google Scholar
  4. 4.
    Biere, A.: Lingeling and friends at the SAT competition 2011. Technical report, FMV Reports Series, Institute for Formal Models and Verification, Johannes Kepler University, Altenbergerstr. 69, 4040 Linz, Austria (2011)Google Scholar
  5. 5.
    Birattari, M., Yuan, Z., Balaprakash, P., Stützle, T.: F-Race and iterated F-Race: an overview. In: Bartz-Beielstein, T., Chiarandini, M., Paquete, L., Preuss, M. (eds.) Experimental Methods for the Analysis of Optimization Algorithms, pp. 311–336. Springer, Heidelberg (2010). CrossRefGoogle Scholar
  6. 6.
    Braunstein, A., Mézard, M., Zecchina, R.: Survey propagation: an algorithm for satisfiability. Random Structures & Algorithms 27(2), 201–226 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Fukunaga, A.: Efficient implementations of SAT local search. In: Seventh International Conference on Theory and Applications of Satisfiability Testing (SAT 2004), pp. 287–292 (2004, this volume)Google Scholar
  8. 8.
    bwGRiD( Member of the German D-Grid initiative, funded by the Ministry of Education and Research (Bundesministeriumfür Bildung und Forschung) and the Ministry for Science, Research and Arts Baden-Württemberg (Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg). Techical report, Universities of Baden-Württemberg (2007-2010)
  9. 9.
    Hoos, H.H.: An adaptive noise mechanism for WalkSAT. In: Proceedings of the Eighteenth National Conference in Artificial Intelligence (AAAI 2002), pp. 655–660 (2002)Google Scholar
  10. 10.
    Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco (2005)zbMATHGoogle Scholar
  11. 11.
    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). doi: 10.1007/978-3-642-14186-7_31 CrossRefGoogle Scholar
  12. 12.
    Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. In: ISTCS, pp. 128–133 (1993).
  13. 13.
    McAllester, D., Selman, B., Kautz, H.: Evidence for invariants in local search. In: Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI 1997), pp. 321–326 (1997)Google Scholar
  14. 14.
    Papadimitriou, C.H.: On selecting a satisfying truth assignment. In: Proceedings of the 32nd Annual Symposium on Foundations of Computer Science (FOCS 1991), pp. 163–169 (1991)Google Scholar
  15. 15.
    Schöning, U.: A probabilistic algorithm for \(k\)-SAT and constraint satisfaction problems. In: Proceedings of the Fourtieth Annual Symposium on Foundations of Computer Science (FOCS 1999), p. 410 (1999)Google Scholar
  16. 16.
    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). doi: 10.1007/978-3-540-73554-0_17 CrossRefGoogle Scholar
  17. 17.
    Seitz, S., Alava, M., Orponen, P.: Focused local search for random 3-satisfiability. CoRR abs/cond-mat/0501707 (2005)Google Scholar
  18. 18.
    Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures, 4th edn. Chapman & Hall/CRC, Boca Raton (2007)zbMATHGoogle Scholar
  19. 19.
    Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998).
  20. 20.
    Tompkins, D.A.D.: Dynamic local search for SAT: design, insights and analysis. Ph.D. thesis, University of British Columbia, October 2010Google Scholar
  21. 21.
    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). doi: 10.1007/978-3-642-21581-0_24 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Institute of Theoretical Computer ScienceUlm UniversityUlmGermany

Personalised recommendations