Applying aspiration in local search for satisfiability.

Cong Peng,Zhongwei Xu,Meng Mei,Baogui Xin

doi:10.1371/journal.pone.0231702

Cong Peng, Zhongwei Xu + Show 2 more

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https://doi.org/10.1371/journal.pone.0231702

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Journal: PloS one	Publication Date: Apr 23, 2020
Citations: 3	License type: CC BY 4.0

Affiliation: Leiden University, Tongji University

Abstract

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.

Highlights

The Boolean satisfiability (SAT) problem is one of the most studied NP-complete problems, and is of significant importance in both theory and pracite [1]
On the last instance family which is the most difficult instance family to be solved (k3-v50000), the success rates of AspiSAT, Swqcc and Sparrow are 100%, 99.8%, 73.3% and 0.0% respectively. This shows that the performance of Sparrow and gNovelty+GCwa is significantly lower than AspiSAT and Swqcc
In order to better illustrate the performance gap between AspiSAT and Swqcc and the performance gap between the QCCA heuristic and the original quantitative configuration checking (QCC) heuristic, we further explore the performance of our AspiSAT solver and the Swqcc solver on a larger-scale random 3-SAT instances (110000 ⩽ ]var ⩽ 150000)

Summary

Introduction

The Boolean satisfiability (SAT) problem is one of the most studied NP-complete problems, and is of significant importance in both theory and pracite [1]. The SAT problem is to decide whether there exists a complete assignment that satisfies all clauses in F Since these three SLS solvers (namely AspiSAT, Ptwqcc and AspiPT) proposed in this paper are all dynamic local search algorithms, here we give an brief introduction of related concepts of dynamic local search. Combining quantitative configuration checking heuristics with aspiration mechanism the QCC heuristic achieves improvement over the original CC heuristic, according to the implementation details described in [33], the QCC heuristic, which is similar to the original CC heuristic, still makes SLS algorithms ignore flipping a number of variables with relatively large score(x) when reaching the local optima. The algorithm selects the variable to be flipped according to the selection mechanisms employed in the greedy mode and the diversification mode of the QCCA heuristic.

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Evaluation results

Conclusion