Time-dependent vehicle-UAV path optimization for urban dynamic traffic restriction and no-fly zone

This study formulates a time-dependent vehicle–UAV joint routing problem (TDVRPD-VRZ-NFZ) for Wuhan’s urban distribution, capturing the interaction between diurnal traffic dynamics and Vehicle-Restricted Zones (VRZs) as well as No-Fly Zones (NFZs). The objective minimizes a composite cost comprising energy expenditure (vehicle and UAV), dispatch charges, and tardiness penalties. The problem is cast as a mixed-integer program that integrates time-dependent travel, regulatory detours, and energy coupling. Specifically, (i) an intra-day speed curve is fitted from peak-period statistics and inverted to obtain arc times; (ii) tangent (VRZ) and edge-tracking (NFZ) detour models are constructed; and (iii) energy models for electric vehicles and rotary-wing UAVs are incorporated. To address large-scale instances, a hybrid solver (IHGA-VNS-SL) is developed, combining GA for diversity preservation, VNS for targeted refinement, and a simulated-annealing acceptance rule. Feasibility repair with adaptive penalties is applied, while a self-learning scheduler tunes crossover, mutation, and neighborhood probabilities. On Wuhan instances calibrated with regulatory windows and time-varying traffic, IHGA-VNS-SL yields lower total cost and faster convergence than GA and GA + VNS; under tight time windows it further reduces tardiness and energy consumption while preserving feasibility and stability. Ablation experiments indicate substantial degradation when SA or self-learning is removed; sensitivity analyses further reveal that time-varying speeds suppress delays, that VRZ/NFZ primarily reshapes timing rather than mileage or energy, and that larger tardiness weights curb violations effectively. Overall, the findings indicate a close alignment between the model and urban regulatory/energy mechanisms, and demonstrate the scalability and robustness of the proposed scheduler for air–ground cooperative distribution in megacities. Limitations include deterministic demand and environment assumptions, a single-depot setting, and simplified UAV energy/geometry. Future work will extend to multi-depot and heterogeneous fleets, incorporate stochastic and online re-optimization with real-time regulatory updates, and refine energy models.