Backbone Guided Extremal Optimization for the Hard Maximum Satisfiability Problem

The original Extremal Optimization (EO) algorithm and its modified versions have been successfully applied to a variety of NP-hard optimization problems. However, there exists a problem that almost all existing EO-based algorithms have overlooked the inherent structural properties behind the optimization problems, e.g., the backbone information. This paper proposes a novel stochastic search method called “Backbone Guided Extremal Optimization (BGEO)” to solve the hard maximum satisfiability (MAX-SAT) problem, one of typical NP-hard combinatorial optimization problems. The basic idea behind BGEO is to incorporate the backbone information into EO to guide the entire search process approaching the optimal solutions. The experimental results on many reported hard MAX-SAT instances have shown the superiority of BGEO to the reported EO-based algorithm without backbone information.