An effective heuristic algorithm for the maximum satisfiability problem

摘要

Stochastic local search algorithms (SLS) have been increasingly applied to approximate solutions of the weighted maximum satisfiability problem (MAXSAT), a model for solutions of major problems in AI and combinatorial optimization. While MAXSAT instances have generally a strong intrinsic dependency between their variables, most of SLS algorithms start the search process with a random initial solution where the value of each variable is generated independently with the same uniform distribution. In this paper, we propose a new SLS algorithm for MAXSAT based on an unconventional distribution known as the Bose-Einstein distribution in quantum physics. It provides a stochastic initialization scheme to an efficient and very simple heuristic inspired by the co-evolution process of natural species and called Extremal Optimization (EO). This heuristic was introduced for finding high quality solutions to hard optimization problems such as colouring and partitioning. We examine the effectiveness of the resulting algorithm by computational experiments on a large set of test instances and compare it with some of the most powerful existing algorithms. Our results are remarkable and show that this approach is appropriate for this class of problems.