Multilevel Stochastic Local Search for SAT

Satisfiability (SAT) problems are a hot topic in the field of combinatorial optimization, having strong theoretical foundations as well as many practical applications. Moreover, approximate SAT algorithms have gained widespread attention because they offer a computationally feasible approach to finding high-quality solutions to NP-hard problems in a scalable and efficient manner. Complete SAT algorithms, which are guaranteed to find a solution in bounded time (if one exists), are particularly important when a guaranteed solution is required, but are of limited practical use because of exponential worst-case bounds. In this paper we propose a Multilevel Stochastic Local Search (MLSLS) algorithm that combines power of a complete algorithm with the efficiency and scalability of a Stochastic Local Search (SLS) method. We probabilistically assign values to a varying-sized subset of the variables and then use an efficient unit-propagation algorithm to produce a coarsened approximation of the original problem instance. We then construct an initial candidate solution from the reduced SAT formula and perform a subsequent local search using a state-of-the-art stochastic local search algorithm. Results achieved from our experiments showed our algorithm to be slower than the competitors, but through empirical testing we have determined the bottleneck to be the systematic component, and with future work directed at improving its efficiency, we believe that positive results are a realistic possibility.