Initial Solution Generation and Diversified Variable Picking in Local Search for (Weighted) Partial MaxSAT

Abstract

The (weighted) partial maximum satisfiability ((W)PMS) problem is an important generalization of the classic problem of propositional (Boolean) satisfiability with a wide range of real-world applications. In this paper, we propose an initialization and a diversification strategy to improve local search for the (W)PMS problem. Our initialization strategy is based on a novel definition of variables’ structural entropy, and it aims to generate a solution that is close to a high-quality feasible one. Then, our diversification strategy picks a variable in two possible ways, depending on a parameter: continuing to pick variables with the best benefits or focusing on a clause with the greatest penalty and then selecting variables probabilistically. Based on these strategies, we developed a local search solver dubbed ImSATLike, as well as a hybrid solver ImSATLike-TT, and experimental results on (weighted) partial MaxSAT instances in recent MaxSAT Evaluations show that they outperform or have nearly the same performances as state-of-the-art local search and hybrid competitors, respectively, in general. Furthermore, we carried out experiments to confirm the individual impacts of each proposed strategy.