An Iterative Path-Breaking Approach with Mutation and Restart Strategies for the MAX-SAT Problem

TL;DR

This paper introduces IPBMR, a novel local search algorithm for MAX-SAT that combines path-breaking, mutation, restart strategies, and stochastic steps, outperforming current leading solvers.

Contribution

It proposes a new MAX-SAT algorithm integrating path-breaking, mutation, and restart strategies, addressing limitations of Path-Relinking in this domain.

Findings

IPBMR outperforms two state-of-the-art MAX-SAT solvers.

The path-breaking strategy effectively avoids unpromising search regions.

Mutation and restart strategies enhance search diversification.

Abstract

Although Path-Relinking is an effective local search method for many combinatorial optimization problems, its application is not straightforward in solving the MAX-SAT, an optimization variant of the satisfiability problem (SAT) that has many real-world applications and has gained more and more attention in academy and industry. Indeed, it was not used in any recent competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a new local search algorithm called IPBMR for the MAX-SAT, that remedies the drawbacks of the Path-Relinking method by using a careful combination of three components: a new strategy named Path-Breaking to avoid unpromising regions of the search space when generating trajectories between two elite solutions; a weak and a strong mutation strategies, together with restarts, to diversify the search; and stochastic path generating steps to avoid premature local optimum solutions. We then present experimental results to show that IPBMR outperforms two of the best state-of-the-art MAX-SAT solvers, and an empirical investigation to identify and explain the effect of the three components in IPBMR.