Choosing probability distributions for stochastic local search and the role of make versus break

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. © 2012 Springer-Verlag.