Solving the maximum satisfiability problem by fuzzy converting it into a continuous optimization problem

Abstract

The satisfiability problem is the first problem proved to be NP-Complete and has been one of the core NP-Complete problems since then. The satisfiability problem is a decision problem. And the maximum satisfiability problem is its optimization version that aims to find an assignment that satisfies most clauses. In this study, a fuzzy conversion method is proposed to convert the maximum satisfiability problem into a continuous optimization problem. Then the continuous optimization problem is solved by the multiple trajectory search that was previously proposed by us. The proposed fuzzy conversion method transforms the discrete search space into the continuous search space. Furthermore, the fitness function defined on this continuous search space is itself continuous. This fact makes the search much easier. An experiment was conducted to evaluate the performance of the proposed method. Comparison with several methods published in the literature reveals that the proposed method is promising.