Leader–Follower Optimizer

This work proposes the Leader–Follower Optimizer (LFO), a novel population-based meta-heuristic for global optimization inspired by explicit social leader–follower interaction dynamics. Unlike conventional approaches based on a single reference solution or homogeneous influence structures, the LFO introduces a dynamic hierarchy composed of multiple leaders with different levels of influence, allowing the search process to be guided simultaneously by several promising solutions. The method incorporates an influence operator applied both to leader–follower interactions and to interactions among the leaders themselves, promoting cooperation, diversity preservation, and progressive refinement of high-quality solutions. The performance of the LFO is evaluated using 25 classical benchmark functions, including unimodal, multimodal, and fixed-dimension multimodal problems, and compared with Simulated Annealing, Genetic Algorithm, Differential Evolution, Adaptive Differential Evolution with Optional External Archive (JADE), Success-History Adaptive Differential Evolution with Linear Population Size Reduction (L-SHADE), Particle Swarm Optimization, Grey Wolf Optimizer, Whale Optimization Algorithm, Fungal Growth Optimizer, and Dhole Optimization Algorithm. The results show that the LFO consistently outperforms classical methods and remains highly competitive with recent state-of-the-art optimizers, achieving Friedman average ranks of 4.76 for the average criterion and 4.44 for the minimum-value criterion over the complete benchmark suite, with statistically significant differences among methods. The method is also applied to PID controller tuning in two control engineering problems: thermal boiler temperature regulation and electric vehicle cruise control. In both cases, the LFO achieved optimal or near-optimal solutions, obtaining the best average performance in the thermal control problem (JT= 14.1240) and matching the best results in the electric vehicle cruise control problem (Jv= 4.7733), while maintaining high robustness and low variability across independent runs. These results demonstrate that the LFO is a robust and versatile optimization method with strong potential for benchmark optimization and real-world control engineering applications.