Multi-UAV cooperative path planning based on multi-strategy enhanced multi-objective phototropic growth algorithm

To address the bottlenecks faced by traditional ground transportation in hilly terrain due to topographical constraints, this study proposes a multi-strategy Enhanced Multi-Objective Phototropic Growth Algorithm (EMOPGA) to tackle the challenges of multi-Unmanned Aerial Vehicles (UAV) cooperative transport for material delivery tasks. This approach aims to overcome the limitations of standard Phototropic Growth Algorithm (PGA), such as susceptibility to local optima and suboptimal initial population quality. It constructs an optimization framework by integrating chaotic mapping for initialization, Lévy flight mutation operators, and an environmental selection mechanism based on Pareto dominance and elite retention strategies. Simulation experiments across nine scenarios demonstrate that EMOPGA achieves a 112.11% improvement in the Average Hypervolume (HV) metric and a 43.11% reduction in the Spacing (SP) metric compared to MOPGA. In comparative experiments against 11 representative algorithms in the complex scenario, EMOPGA achieved an average HV of 9.31 × 10¹³ and an average SP of 0.0322. Specifically, EMOPGA achieves a 29.1% HV improvement over MOPGA (the best HV baseline) and a 75.0% SP reduction relative to MOEA/D (the best SP baseline). EMOPGA provides an efficient optimization paradigm for multi-UAV path planning in complex terrain, combining high convergence, strong uniformity, and robust performance. It demonstrates significant potential for practical applications in logistics and emergency response.