Novel swarm intelligence method for multimodal optimization: Sheep flock migrate optimization algorithm

Swarm intelligence optimization algorithms have garnered considerable attention for solving real-world optimization problems owing to their ability to emulate collective behaviors such as the movement, interaction, and evolution observed in biological swarms. In this paper, we propose a novel bionic swarm intelligence optimization method called the sheep flock migrate optimization (SFMO) algorithm, which is inspired by the intermittent collective motion behavior exhibited by sheep. The SFMO algorithm comprises grazing operator, collective motion operator, and compensation strategy. The grazing operator is formulated based on mathematical models that capture the local foraging behavior of sheep within a confined range. This operator is inspired by the “two-phase motion of sheep”, as well as the widely recognized “green wave chasing” mechanism observed in herbivores. The grazing operator, which is responsible for the local search functionality, enhances the algorithm’s exploitation capability, thereby enhancing its ability to effectively exploit the search space. The collective motion operator builds upon the “two-phase motion mechanism” and incorporates the “leader–follower” mechanism observed during the movement of a sheep flock. By simulating the overall migration behavior of a sheep flock, this operator assumes the role of global search and aims to enhance the algorithm’s exploration ability. The compensation strategy temporarily expands the search range by leveraging the social learning mechanism observed in flock behavior, thereby improving the algorithm’s ability to escape from local optima. Distinguished from the existing swarm intelligence-based optimization methods, the SFMO algorithm alternately executes the grazing operator and collective motion operator, mirroring the intermittent collective motion mechanism exhibited by flocks. The compensation mechanism is adaptively triggered when the algorithm is likely to converge to a local optimal solution, ensuring a balance between the exploration and exploitation capabilities. SFMO introduces a novel and efficient optimizer in the field of population intelligence optimization by mitigating the probability of falling into local optima through extensive stochastic search-guided population migration and an expanded search mechanism during migration stagnation. The convergence proof and complexity analysis results of the SFMO algorithm provide theoretical support for its feasibility and effectiveness. To further validate the proposed method, we conduct numerical simulations using CEC-2017 benchmark functions and compare SFMO with representative optimization algorithms, namely, pigeon-inspired optimization (PIO), particle swarm optimization (PSO), and gray wolf optimizer (GWO), under equivalent conditions. The simulation results demonstrate that SFMO effectively solves function optimization problems and offers considerable advantages, particularly in the context of multimodal function optimization. Among the four algorithms, SFMO demonstrates superior search efficiency, stability, and accuracy. Moreover, it exhibits remarkable advantages in addressing high-dimensional optimization problems, showcasing the highest level of robustness compared with the other algorithms.