Recent advances in the Horse herd optimization algorithm, its versions, and applications

The Horse Herd Optimization Algorithm (HOA) is one of the most recent metaheuristic algorithms reported in the literature, inspired by the herding behavior of horses. Grazing, hierarchy, sociability, imitation, defense mechanisms, and wandering are the six main social behaviors at different ages formulated in this algorithm. Due to its simplicity, flexibility, ability to balance exploration and exploitation, and ability to avoid local optima, this algorithm has attracted the attention of researchers in the optimization domain to solve many problems. This research provides a comprehensive review of the HOA, covering its development from its introduction in 2021 to the data collection date in 2025, as well as its inspiration, mathematical design, and research development. The review also investigates the suggested enhancements proposed by the researchers to improve the performance of the HOA when applied to solve optimization problems across various search spaces and complexities. Furthermore, the different application domains such as engineering, scheduling, image processing, and machine learning are summarized and analyzed. The programming codes and online lectures related to HOA published on scientific portals are also highlighted in the current review. The review also critically evaluates the HOA convergence behavior, identifying its strengths and limitations. The limitations of the HOA are also discussed, and new research directions are provided for future research. This review provides valuable guidance for researchers by highlighting the HOA’s limitations, suggesting improvements to enhance its performance, and identifying potential scientific areas that could be addressed using the HOA.