Old techniques in new ways: Clause weighting, unit propagation and hybridization for maximum satisfiability

Abstract

Maximum Satisfiability (MaxSAT) is a basic and important constraint optimization problem. When dealing with both hard and soft constraints, the MaxSAT problem is referred to as Partial MaxSAT, which has been used to effectively solve many combinatorial optimization problems in real world. The local search method and the SAT-based method are two popular methods for Partial MaxSAT. Nevertheless, local search algorithms have been dominated by SAT-based algorithms on industrial benchmarks. This work develops an effective local search algorithm for industrial benchmarks, which for the first time is competitive with SAT-based algorithms on industrial MaxSAT benchmarks.We propose a local search algorithm, called SATLike, which exploits the structure of Partial MaxSAT by a novel clause weighting scheme. Then we improve SATLike by integrating a unit propagation based decimation algorithm to generate initial solutions, leading to an improved algorithm, called SATLike 2.0. We also refine SATLike 2.0 and obtain SATLike 3.0. Furthermore, we apply SATLike 3.0 to improve two SAT-based solvers, leading to two hybrid MaxSAT solvers that push the state of the art in MaxSAT solving.Experiments on benchmarks from the MaxSAT Evaluations 2017 and 2018 show that SATLike significantly outperforms previous local search solvers on all the benchmarks. More importantly, SATLike 3.0 has better performance than state-of-the-art SAT-based solvers on unweighted industrial benchmarks. The two hybridized solvers obtain significant improvements on both unweighted and weighted benchmarks.