The maximum satisfiability (MAX-SAT) problem, especially the weighted version, has extensive applications. Weighted MAX-SAT instances encoded from real-world applications may be very large, which calls for efficient approximate methods, mainly stochastic local search (SLS) ones. However, few works exist on SLS algorithms for weighted MAX-SAT. In this paper, we propose a new heuristic called CCM for weighted MAX-SAT. The CCM heuristic prefers to select a CCMP variable. By combining CCM with random walk, we design a simple SLS algorithm dubbed CCLS for weighted MAX-SAT. The CCLS algorithm is evaluated against a state-of-the-art SLS solver IRoTS and two state-of-the-art complete solvers namely akmaxsat_ls and New WPM2, on a broad range of weighted MAX-SAT instances. Experimental results illustrate that the quality of solution found by CCLS is much better than that found by IRoTS, akmaxsat_ls and New WPM2 on most industrial, crafted and random instances, indicating the efficiency and the robustness of the CCLS algorithm. Furthermore, CCLS is evaluated in the weighted and unweighted MAX-SAT tracks of incomplete solvers in the Eighth Max-SAT Evaluation (Max-SAT 2013), and wins four tracks in this evaluation, illustrating that the performance of CCLS exceeds the current state-of-the-art performance of SLS algorithms on solving MAX-SAT instances.

Two-mode stochastic local search (SLS) and focused random walk (FRW) are the two most influential paradigms of SLS algorithms for the propositional satisfiability (SAT) problem. Recently, an interesting idea called configuration checking (CC) was proposed to handle the cycling problem in SLS. The CC idea has been successfully used to improve SLS algorithms for SAT, resulting in state-of-the-art solvers. Previous CC strategies for SAT are based on neighboring variables, and prove successful in two-mode SLS algorithms. However, this kind of neighboring variables based CC strategy is not suitable for improving FRW algorithms. In this paper, we propose a new CC strategy which is based on clause states. We apply this clause states based CC (CSCC) strategy to both two-mode SLS and FRW paradigms. Our experiments show that the CSCC strategy is effective on both paradigms. Furthermore, our developed FRW algorithms based on CSCC achieve state-of-the-art performance on a broad range of random SAT benchmarks.

Stochastic local search (SLS) algorithms have shown effectiveness on satisfiable instances of the Boolean satisfiability (SAT) problem. However, their performance is still unsatisfactory on random k-SAT at the phase transition, which is of significance and is one of the empirically hardest distributions of SAT instances. In this paper, we propose a new heuristic called DCCA, which combines two configuration checking (CC) strategies with different definitions of configuration in a novel way. We use the DCCA heuristic to design an efficient SLS solver for SAT dubbed DCCASat. The experiments show that the DCCASat solver significantly outperforms a number of state-of-the-art solvers on extensive random k-SAT benchmarks at the phase transition. Moreover, DCCASat shows good performance on structured benchmarks, and a combination of DCCASat with a complete solver achieves state-of-the-art performance on structured benchmarks.