On the Quality and Quantity of Random Decisions in Stochastic Local Search for SAT

  • Dave A. D. Tompkins
  • Holger H. Hoos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4013)


Stochastic local search (SLS) methods are underlying some of the best-performing algorithms for certain types of SAT instances, both from an empirical as well as from a theoretical point of view. By definition and in practice, random decisions are an essential ingredient of SLS algorithms. In this paper we empirically analyse the role of randomness in these algorithms. We first study the effect of the quality of the underlying random number sequence on the behaviour of well-known algorithms such as Papadimitriou’s algorithm and Adaptive Novelty+. Our results indicate that while extremely poor quality random number sequences can have a detrimental effect on the behaviour of these algorithms, there is no evidence that the use of standard pseudo-random number generators is problematic. We also investigate the amount of randomness required to achieve the typical behaviour of these algorithms using derandomisation. Our experimental results indicate that the performance of SLS algorithms for SAT is surprisingly robust with respect to the number of random decisions made by an algorithm.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, San Francisco (2004)Google Scholar
  2. 2.
    Papadimitriou, C.H.: On selecting a satisfying truth assignment. In: Proc. of the 32nd Symp. on Foundations of Computer Science, pp. 163–169 (1991)Google Scholar
  3. 3.
    Selman, B., Kautz, H.A., Cohen, B.: Noise strategies for improving local search. In: Proc. of the 12th Nat’l Conf. on Artificial Intelligence (AAAI 1994), pp. 337–343 (1994)Google Scholar
  4. 4.
    Schöning, U.: A probabilistic algorithm for k-SAT and constraint satisfaction problems. In: Proc. of the 40th Symp. on Foundations of Computer Science, pp. 410–414 (1999)Google Scholar
  5. 5.
    Hutter, F., Tompkins, D.A., Hoos, H.H.: Scaling and probabilistic smoothing: Efficient dynamic local search for SAT. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, Springer, Heidelberg (2002)Google Scholar
  6. 6.
    Éric, D.: Taillard: Robust taboo search for the quadratic assignment problem. Parallel Computing 17, 443–455 (1991)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Gent, I.P., Walsh, T.: Towards an understanding of hillclimbing procedures for SAT. In: Proc. of the 11th Nat’l Conf. on Artificial Intelligence (AAAI 1993), pp. 28–33 (1993)Google Scholar
  8. 8.
    Ferrenberg, A.M., Landau, D.P., Wong, Y.J.: Monte Carlo simulations: Hidden errors from “good” random number generators. Physical Review Letters 69, 3382–3384 (1992)CrossRefGoogle Scholar
  9. 9.
    Bauke, H., Mertens, S.: Pseudo random coins show more heads than tails. Journal of Statistical Physics 114, 1149–1169 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ribeiro, C.C., Souza, R.C., Vieira, C.E.C.: A comparative computational study of random number generators. Pacific Journal of Optimization 1, 565–578 (2005)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Tompkins, D.A.D., Hoos, H.H.: Warped landscapes and random acts of SAT solving. In: Proc. of the 8th Symp. on Artificial Intelligence and Mathematics (2004)Google Scholar
  12. 12.
    Iwama, K., Tamaki, S.: Improved upper bounds for 3-SAT. In: Proc. of the 15th ACM-SIAM Symp. on Discrete algorithms (SODA 2004), pp. 328–328 (2004)Google Scholar
  13. 13.
    Parkes, A.J., Walser, J.P.: Tuning local search for satisfiability testing. In: Proc. of the 13th Nat’l Conf. on Artificial Intelligence (AAAI 1996), pp. 356–362 (1996)Google Scholar
  14. 14.
    Hoos, H.H.: An adaptive noise mechanism for WalkSAT. In: Proc. of the 18th Nat’l Conf. on Artificial Intelligence (AAAI 2002), pp. 655–660 (2002)Google Scholar
  15. 15.
    Le Berre, D., Simon, L.: 55 solvers in Vancouver: The SAT 2004 competition. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 321–345. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Modeling & Comp. Simulation 8, 3–30 (1998)zbMATHCrossRefGoogle Scholar
  18. 18.
    Hoos, H.H., Stützle, T.: SATLIB: An online resource for research on SAT. In: SAT 2000: Highlights of Satisfiability Research in the year 2000, pp. 283–292 (2000)Google Scholar
  19. 19.
    Bagini, V., Bucci, M.: A design of reliable true random number generator for cryptographic applications. In: Workshop Cryptographic Hardware & Embedded Syst., pp. 204–218 (1999)Google Scholar
  20. 20.
    Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray, J., Vo, S.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. Technical Report 800-22, NIST (2000)Google Scholar
  21. 21.
    Knuth, D.E.: The Art of Computer Programming, vol. 2. Addison-Wesley, Reading (1969)zbMATHGoogle Scholar
  22. 22.
    Schuurmans, D., Southey, F., Holte, R.C.: The exponentiated subgradient algorithm for heuristic boolean programming. In: Proc. of (IJCAI 2001), pp. 334–341 (2001)Google Scholar
  23. 23.
    Dantsin, E., Goerdt, A., Hirsch, E.A., Schöning, U.: Deterministic algorithms for k-SAT based on covering codes & local search. In: Automata, Languages & Prog., pp. 236–247 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dave A. D. Tompkins
    • 1
  • Holger H. Hoos
    • 1
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

Personalised recommendations