Swarm intelligence optimization algorithms are nature-inspired algorithms that leverage the behavioral mechanisms observed in biological swarm movement, interaction, and evolution. These algorithms are known for their exceptional flexibility, adaptability, robustness, and ability to achieve global optimization, making them extensively applied in solving diverse real-world optimization problems. In this study, we draw inspiration from the intermittent collective motion observed in sheep flocks and propose a novel bio-inspired swarm intelligence optimization method called the Sheep Flock Migrate Optimization (SFMO) algorithm. The SFMO algorithm incorporates three core operator modules: the grazing operator, the collective motion operator, and the compensation strategy. By guiding population migration through extensive random search, SFMO effectively mitigates the risk of converging to local optima, distinguishing itself from existing approaches and offering a new solution in the field of swarm intelligence optimization. Convergence analysis and complexity assessment further contribute to the theoretical underpinning of SFMO. Numerical simulations conducted on the CEC-2017 benchmark functions demonstrate the effectiveness of SFMO in solving function optimization problems, particularly exhibiting notable advantages in scenarios involving multi-modal function optimization.