Flower fertilization optimization algorithm with application to adaptive controllers.

This article presents the Flower Fertilization Optimization Algorithm (FFO), a novel bio-inspired optimization technique inspired by the natural fertilization process of flowering plants. The FFO emulates the behavior of pollen grains navigating through the search space to fertilize ovules, effectively balancing exploration and exploitation mechanisms. The developed FFO is theoretically introduced through the article and rigorously evaluated on a diverse set of 32 benchmark optimization problems, encompassing unimodal, multimodal, and fixed-dimension functions. The algorithm consistently outperformed 14 state-of-the-art metaheuristic algorithms, demonstrating superior accuracy, convergence speed, and robustness across all test cases. Also, exploitation, exploration, and parameter sensitivity analyses were performed to have a comprehensive understanding of the new algorithm. Additionally, FFO was applied to optimize the parameters of a Proportional-Integral-Derivative (PID) controller for magnetic train positioning-a complex and nonlinear control challenge. The FFO efficiently fine-tuned the PID gains, enhancing system stability, precise positioning, and improved response times. The successful implementation underscores the algorithm's versatility and effectiveness in handling real-world engineering problems. The positive outcomes from extensive benchmarking and practical application show the FFO's potential as a powerful optimization tool. In applying multi-objective PID controller parameter optimization, FFO demonstrated superior performance with a sum of mean errors of 190.563, outperforming particle swarm optimization (250.075) and dynamic differential annealed optimization (219.629). These results indicate FFO's ability to achieve precise and reliable PID tuning for control systems. Furthermore, FFO achieved competitive results on large-scale optimization problems, demonstrating its scalability and robustness.