Applying aspiration in local search for satisfiability

The Boolean Satisfiability problem (SAT) is a prototypical NP-complete problem, which has been widely studied due to its significant importance in both theory and applications. Stochastic local search (SLS) algorithms are among the most efficient approximate methods available for solving certain types of SAT instances. The quantitative configuration checking (QCC) heuristic is an effective approach for improving SLS algorithms on solving the SAT problem, resulting in an efficient SLS solver for SAT named Swqcc. In this paper, we focus on combining the QCC heuristic with an aspiration mechanism, and then design a new heuristic called QCCA. On the top of Swqcc, we utilize the QCCA heuristic to develop a new SLS solver dubbed AspiSAT. Through extensive experiments, the results illustrate that, on random 3-SAT instances, the performance of AspiSAT is much better than that of Swqcc and Sparrow, which is an influential and efficient SLS solver for SAT. In addition, we further enhance the original clause weighting schemes employed in Swqcc and AspiSAT, and thus obtain two new SLS solvers called Ptwqcc and AspiPT, respectively. The eperimental results present that both Ptwqcc and AspiPT outperform Swqcc and AspiSAT on random 5-SAT instances, indicating that both QCC and QCCA heuristics are able to cooperate effectively with different clause weighting schemes.