Local Optima Network Analysis for MAX-SAT

Abstract

Local Optima Networks (LONs) are a valuable tool to understand fitness landscapes of optimization problems observed from the perspective of a search algorithm. Local optima of the optimization problem are linked by an edge in LONs when an operation in the search algorithm allows one of them to be reached from the other. Previous work analyzed several combinatorial optimization problems using LONs and provided a visual guide to understand why the instances are difficult or easy for the search algorithms. In this work we analyze for the first time the MAX-SAT problem. Given a Boolean formula in Conjunctive Normal Form, the goal of the MAX-SAT problem is to find an assignment maximizing the number of satistified clauses. Several random and industrial instances of MAX-SAT are analyzed using Iterated Local Search to sample the search space.