A Probability Distribution Strategy with Efficient Clause Selection for Hard Max-SAT Formulas

Many real-world problems involving constraints can be regarded as instances of the Max-SAT problem, which is the optimization variant of the classic satisfiability problem. In this paper, we propose a novel probabilistic approach for Max-SAT called ProMS. Our algorithm relies on a stochastic local search strategy using a novel probability distribution function with two strategies for picking variables, one based on available information and another purely random one. Moreover, while most previous algorithms based on WalkSAT choose unsatisfied clauses randomly, we introduce a novel clause selection strategy to improve our algorithm. Experimental results illustrate that ProMS outperforms many state-of-the-art stochastic local search solvers on hard unweighted random Max-SAT benchmarks.