Pure MaxSAT and Its Applications to Combinatorial Optimization via Linear Local Search.

Maximum Satisfiability (MaxSAT) is a general model for formulating combinatorial optimization problems. MaxSAT formulas encoded from different domains have different features, yet most MaxSAT solvers are designed for general formulas. This work considers an important subclass of MaxSAT, named as Pure MaxSAT, which characterizes a wide range of combinatorial optimization problems particularly subset problems. We design a novel local search method for Pure MaxSAT, which combines the idea of linear search and local search and is dubbed as linear local search. Our algorithm LinearLS significantly outperforms state of the art MaxSAT solvers on Pure MaxSAT instances, including instances from MaxSAT Evaluations and those encoded from three famous NP hard combinatorial optimization problems. Moreover, LinearLS outperforms state of the art algorithms for each tested combinatorial optimization problem on the popular benchmarks.