Firefly algorithm: overview, applications, and modifications

The Firefly Algorithm (FA) is a nature-inspired, population-based metaheuristic developed by Xin-She Yang in 2007 that mimics the flashing behavior of fireflies. This paper presents an in-depth investigation of the Firefly Algorithm, beginning with its biological inspiration and mathematical formulation, and proceeding to a comprehensive discussion of its diverse applications across engineering, image segmentation, scheduling, and other domains. In addition, various modifications of the original FA including Gaussian variants, chaotic variants, and opposition- and dimensional-based improvements are reviewed and compared. Two detailed tables summarize the primary applications and modifications, respectively, while discussions highlight the trade-offs between exploration and exploitation inherent in the algorithm. The paper concludes with an analysis of current achievements and future research directions in firefly-based optimization techniques.