Improving Implementation of SLS Solvers for SAT and New Heuristics for k-SAT with Long Clauses

Abstract

Abstract. Stochastic Local Search (SLS) solvers are considered one of the best solving technique for randomly generated problems and more recently also have shown great promise for several types of hard combinatorial problems. Within this work, we provide a thorough analysis of different implementation variants of SLS solvers on random and on hard combinatorial problems. By analyzing existing SLS implementations, we are able to discover new improvements inspired by CDCL solvers, which can speed up the search of all types of SLS solvers. Further, our analysis reveals that the multilevel break values of variables can be easily computed and used within the decision heuristic. By augmenting the probSAT solver with the new heuristic, we are able to reach new stateof-the-art performance on several types of SAT problems, especially on those with long clauses. We further provide a detailed analysis of the clause selection policy used in focused search SLS solvers.

Stochastic Local Search for Satisfiability Modulo Theories

“…However, recent work shows that clause selection has a strong impact on the performance of WalkSAT algorithms and random selection is sometimes suboptimal. For example, breadth-first selection heuristics sometimes achieve better results (Balint et al 2014). Still, clause selection has to be rather simple because SLS solvers for SAT often perform several million moves per second.…”

“…Running some preliminary experiments showed that it is frequently better to select assertions that already have a high score (i.e., are almost satisfied). Given the results from (Balint et al 2014), it is likely that some diversification is beneficial as well. Therefore, we use a heuristic inspired by the field of bandit theory used in the UCB (Upper Confidence Bounds) algorithm (Agrawal 1995).…”

“…Further, evaluating the score function implies updating the whole formula. This is again in contrast to SAT, where the score change is either cached or easy to compute on the fly (Balint et al 2014). Evaluating possible moves therefore is the bottleneck of our current implementation.…”

Local Search for Hard SAT Formulas: The Strength of the Polynomial Law

“…Observation 1. (Balint et al 2014) During the focused random walk for uniform random k-CNF (k = 3, 4, 5, 6, 7) with ratio r k , about 90% break values encountered for variables within the chosen unsatisfied clauses are less than 5, while a constant fraction of break values can reach up to r k k/2.…”

An Efficient Implementation for WalkSAT

“…Implementation affects the performances of SLS algorithm very much. The latest version of probSAT uses caching scheme with XOR technology [1], while WalkSAT in UBCSAT framework [4] and the latest version of WalkSATlm [2] are under non-caching implementation. In this section, we propose a more efficient implementation called separated-non-caching.…”