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

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.