Solving the MAX-SAT problem by binary enhanced fireworks algorithm

In this paper, we present a binary enhanced firework algorithm (BEFWA) for optimization problems with a search space of binary vectors, and we test this new algorithm for the MAX-SAT problem. The EFWA algorithm is a relatively recent development in swarm intelligence (SI) for continuous optimization, and the explosion amplitude operator in EFWA does not fit for searching a good solution in a discrete binary space. The original ABC algorithm is also not suitable for searching through a binary space, but its adaptation, the discrete ABC (DisABC), for a binary space was recently presented. In the present paper, we employ the similarity-measure-based differential expression from DisABC to design the binary EFWA algorithm to operate in binary space. The MAX-SAT is a well-known modelling framework for various computationally challenging problems, and thus it has many applications. However, the MAX-SAT problem has been proven to be NP-hard. Existing results indicate that evolutionary algorithms (EAs) can be useful for finding good-quality solutions without excessive computational resources. Our experimental results demonstrate that the binary EFWA can be a better choice over DisABC and Genetic Algorithm (GA) for various classes of MAX-SAT instances.