Hybrid fertilized particle swarm optimization for engineering design with application to vibration control

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.