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An effective heuristic algorithm for the maximum satisfiability problem

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Abstract

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.

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Authors and Affiliations

  1. Computer Science Department, University of Tébessa, Tébessa, 12000, Algeria

    Mohamed El Bachir Menaï

  2. Computer Science Department, Mentouri University of Constantine, Constantine, 25000, Algeria

    Mohamed Batouche

Authors
  1. Mohamed El Bachir Menaï
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  2. Mohamed Batouche
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Correspondence to Mohamed El Bachir Menaï.

Additional information

Mohamed El Bachir Menaï received his M.S. and Ph.D. degrees in computing systems from the University of Annaba and Mentouri University of Constantine, respectively. He is currently an assistant professor at the Computer Science Department of the University of Tébessa. His main interests are in the areas of problem complexity, heuristic search, evolutionary computation and quantum computing.

Mohamed Batouche received his M.S. and Ph.D. degrees in computer science from the Institut National Polytechnique de Lorraine (INPL), France, in 1989 and 1993, respectively. Currently, he is a professor at the University of Constantine, Algeria. His research areas include artificial intelligence and pattern recognition.

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Menaï, M.E.B., Batouche, M. An effective heuristic algorithm for the maximum satisfiability problem. Appl Intell 24, 227–239 (2006). https://doi.org/10.1007/s10489-006-8514-7

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