Pigeon-Inspired Optimization Algorithm: Definition, Variants, and Its Applications in Unmanned Aerial Vehicles

The Pigeon-Inspired Optimization (PIO) algorithm constitutes a metaheuristic method derived from the homing behaviour of pigeons. Initially formulated for three-dimensional path planning in unmanned aerial vehicles (UAVs), the algorithm has attracted considerable academic and industrial interest owing to its effective balance between exploration and exploitation, coupled with advantages in real-time performance and robustness. Nevertheless, as applications have diversified, limitations in convergence precision and a tendency toward premature convergence have become increasingly evident, highlighting a need for improvement. This review systematically outlines the developmental trajectory of the PIO algorithm, with a particular focus on its core applications in UAV navigation, multi-objective formulations, and a spectrum of variant models that have emerged in recent years. It offers a structured analysis of the foundational principles underlying the PIO. It conducts a comparative assessment of various performance-enhanced versions, including hybrid models that integrate mechanisms from other optimization paradigms. Additionally, the strengths and weaknesses of distinct PIO variants are critically examined from multiple perspectives, including intrinsic algorithmic characteristics, suitability for specific application scenarios, objective function design, and the rigor of the statistical evaluation methodologies employed in empirical studies. Finally, this paper identifies principal challenges within current PIO research and proposes several prospective research directions. Future work should focus on mitigating premature convergence by refining the two-phase search structure and adjusting the exponential decrease of individual numbers during the landmark operator. Enhancing parameter adaptation strategies, potentially using reinforcement learning for dynamic tuning, and advancing theoretical analyses on convergence and complexity are also critical. Further applications should be explored in constrained path planning, Neural Architecture Search (NAS), and other real-world multi-objective problems. For Multi-objective PIO (MPIO), key improvements include controlling the growth of the external archive and designing more effective selection mechanisms to maintain convergence efficiency. These efforts are expected to strengthen both the theoretical foundation and practical versatility of PIO and its variants.