CCEHC-Plus: Reemphasis on Soft Clauses in WPMS Problem based on CCEHC

Abstract

The Weighted MAX-SAT problem (WMS) and Non-weighted Partial MAX-SAT problem (PMS) are two important branches of Maximum Satisfiable Problem (MAX-SAT). The Weighted Partial MAX-SAT (WPMS) problem is a combination of WMS and PMS, which has more important significance in practical applications. In recent years, with the significant breakthroughs of the research on the Configuration Checking (CC) strategy of WMS and PMS problems by Shaowei Cai and others, some advanced solving algorithms such as CCLS [1] and Dist [2] have emerged. On this basis, the CCEHC [3] solving algorithm with the hard clause weighting scheme and biased random walk strategy that specially designed for WPMS instances have achieved more efficient performance. However, the CCEHC solving strategy overly considers the effect of the hard clauses in the solution process. Although the strategies make the solution result closer to the feasible solution, it is difficult to guarantee the optimality of the solution, i.e., minimize total unsatisfied soft clause weight. So, this paper presents an improved CCEHC-Plus solving algorithm based on CCEHC [3]. CCEHC-Plus reconsiders the effect of soft clauses in the solution process and optimizes the original selection strategy in CCEHC. Secondly, during the search steps, the algorithm adjusts the weight of some high-weighted soft clauses which are hard to be satisfied reversibly and optimizes the original weighting scheme. CCEHC-Plus is also optimized for the random walk strategy. A large number of experimental tests show that compared with the CCEHC algorithm, the CCEHC-Plus algorithm can conspicuously improve the quality of the solution in solving industrial and crafted WPMS instances.