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.

The artificial bee colony (ABC) algorithm is a famous swarm intelligence method utilized across various disciplines due to its robustness. However, it exhibits limitations in exploration mechanisms, particularly in high-dimensional or complex landscapes. This article introduces the adaptive exploration artificial bee colony (AEABC), a novel variant that reinspires the ABC algorithm based on real-world phenomena. AEABC incorporates new distance-based parameters and mechanisms to correct the original design, enhancing its robustness. The performance of AEABC was evaluated against 33 state-of-the-art metaheuristics across twenty-five benchmark functions and an engineering application. AEABC consistently outperformed its counterparts, demonstrating superior efficiency and accuracy. In a variable-sized problem (n = 10), the traditional ABC algorithm converged to 3.086 × 10⁶, while AEABC achieved a convergence of 2.0596 × 10⁻²⁵⁵, highlighting its robust performance. By addressing the shortcomings of the traditional ABC algorithm, AEABC significantly advances mathematical optimization, especially in engineering applications. This work underscores the significance of the inspiration of the traditional ABC algorithm in enhancing the capabilities of swarm intelligence.

Structural vibration control is a critical challenge in engineering systems such as tower cranes, where excessive oscillations compromise safety and operational accuracy. This paper proposes a Fertilized Particle Swarm Optimization (FRPSO) algorithm that hybridizes Particle Swarm Optimization with Flower Fertilization Optimization via a dual-phase global-best update to enhance the exploration–exploitation balance. FRPSO is evaluated on 26 problems (20 non-convex constrained cases, four 1000-variable large-scale benchmarks, structural optimization, and a tower crane vibration-control case study) and is compared against 18 metaheuristic optimizers. Across the benchmark suites, FRPSO achieves solution quality with consistent run-to-run stability, achieving near-optimal objective values with very low dispersion in the 1000-variable tests under the reported experimental protocol. In structural optimization, FRPSO reduces the weight of the 72-bar truss from 381.91 lb (PSO) to 379.63 lb. For the tower crane boom modeled as a 3D beam structure under transient dynamic loading, FRPSO yields designs that achieve effective vibration attenuation, as evidenced by the rapid decay of boom-tip vertical displacement responses, while satisfying stress and displacement constraints. Non-parametric statistical comparisons based on the Wilcoxon signed-rank test indicate that the observed improvements are consistent across repeated runs for selected benchmark cases. Overall, the reported results suggest that FRPSO can be effectively applied to vibration-aware structural design of crane booms and other flexible beam-type structures.