Monarch butterfly optimization: A comprehensive review

Abstract Swarm intelligence (SI) is the collective behavior of decentralized, self-organized natural or artificial systems. Monarch butterfly optimization (MBO) algorithm is a class of swarm intelligence metaheuristic algorithm inspired by the migration behavior of monarch butterflies. Through the migration operation and butterfly adjusting operation, individuals in MBO are updated. MBO can outperform many state-of-the-art optimization techniques when solving global numerical optimization and engineering problems. This paper presents a comprehensive review of the MBO algorithm including its modifications, hybridizations, variants, and applications. Additionally, further research directions for MBO are discussed. This review study serves as a solid refence for future studies in the arena of SI and in particular the MBO algorithm.