An Enhanced Plant Growth Algorithm with Adam Learning, Lévy Flight, and Dynamic Stage Control

This study addresses the limitations of the traditional Plant Growth Algorithm (PGA), including insufficient local exploitation, premature convergence, and performance degradation in high-dimensional optimization. To enhance search efficiency, we propose the ALDPGA (Adam–Lévy Dynamic Plant Growth Algorithm), which incorporates Adam-based adaptive gradient learning, Lévy long-tailed perturbation, and a dynamic stage-control mechanism. The method strengthens directional refinement in the light region using gradient-assisted learning and a simulated-annealing rule, while staged hybrid perturbations and adaptive learning-rate scheduling expand early exploration in the shaded region. During the cell-elongation phase, Lévy-driven dynamic trajectories guide the transition from global search to fine-grained convergence. Notably, the light and shaded regions of the algorithm are designed symmetrically, balancing exploration and exploitation. The light region reflects phototropism, fostering growth towards optimal solutions, while the shaded region adapts to explore previously underexplored areas. Extensive experiments on CEC2017, CEC2020, and CEC2022 benchmarks demonstrate improvements in optimal solutions, convergence speed, and statistical stability. Wilcoxon tests confirm the significance of these gains, and ablation studies verify the contributions of each component. ALDPGA’s enhanced robustness and optimization efficiency make it well suited for complex, multimodal, and high-dimensional problems, offering new insights into bio-inspired optimization frameworks.