Efficient Initial Solution to Extremal Optimization Algorithm for Weighted MAXSAT Problem

Stochastic local search algorithms are proved to be one of the most effective approach for computing approximate solutions of hard combinatorial problems. Most of them are based on a typical randomness related to some uniform distributions for generating initial solutions. Particularly, Extremal Optimization is a recent meta-heuristic proposed for finding high quality solutions to hard optimization problems. In this paper, we introduce an algorithm based on another distribution, known as the Bose-Einstein distribution in quantum physics, which provides a new stochastic initialization scheme to an Extremal Optimization procedure. The resulting algorithm is proposed for the approximated solution to an instance of the weighted maximum satisfiability problem (MAX SAT). We examine its effectiveness by computational experiments on a large set of test instances and compare it with other existing meta-heuristic methods. Our results are remarkable and show that this approach is appropriate for this class of problems.