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As an effective tool for the representation and reasoning of uncertain theories, Bayesian networks are widely used in various fields of artificial intelligence. However, learning the optimal Bayesian network structure is an NP-hard problem. The score-and-search approach is a common method for solving the problems associated with Bayesian network structure learning. This paper presents a novel method for learning the structure of a Bayesian network using a discrete firefly optimization algorithm, which has been successfully applied to solve various optimization problems. In the proposed algorithm, each firefly moves in a discrete space based on a redefined movement strategy. Then, the mutation operator is employed to prevent the algorithm from stopping prematurely and falling into a local optimum. Finally, a local optimizer is used to enhance the exploitation ability of the firefly to obtain the best feasible solution. We compared the proposed algorithm with state-of-the-art algorithms on well-known benchmark networks. The experimental results show that the proposed algorithm has better convergence accuracy and higher scores in most cases, compared to other algorithms, indicating that the proposed algorithm can be used as an effective and feasible method for learning Bayesian network structures. [ABSTRACT FROM AUTHOR]