Research on the optimization of delivery routes for vehicles with drones under no-fly zone restrictions

With the rapid development of e-commerce, logistics and distribution systems face the dual pressures of efficiency improvement and cost control. Unmanned Aerial Vehicle (UAV) delivery, featuring flexibility, high efficiency, and low carbon emissions, has become an effective means to solve the "last-mile" problem. However, the widespread no-fly zones in urban environments (e.g., airports, government agencies, and high-voltage power lines) severely limit the application scope of UAVs and increase the complexity of path planning. Against this backdrop, the vehicle-assisted UAV collaborative delivery model has emerged: through the division of labor and collaboration between ground vehicles and UAVs, it not only expands the service radius of UAVs but also overcomes the constraints of no-fly zones, achieving dual improvements in delivery efficiency and service quality.This study focuses on the optimization of vehicle-assisted UAV delivery paths under no-fly zone constraints, aiming to construct a multi-objective optimization model that balances delivery costs, carbon emissions, and customer satisfaction, and to design an efficient solution algorithm for providing scientific decision support to logistics enterprises. First, the paper systematically sorts out the classification and definition of no-fly zones as well as their impact mechanisms on UAV path planning, and elaborates on the theoretical basis of vehicle-UAV collaborative delivery, including the constituent elements of the problem, methods for quantifying customer satisfaction, and the application framework of heuristic algorithms. On this basis, a mixed-integer programming model is built with the objectives of minimizing total cost, minimizing carbon emissions, and maximizing customer satisfaction. Given that this model falls into the category of NP-hard problems, we have designed a four-stage heuristic solution. First, an improved K-means algorithm (IKM) is used to cluster customer points under the constraint of the UAV's maximum flight radius, so as to determine vehicle parking points. Second, a multi-objective genetic algorithm is applied to plan UAV delivery routes for customers in open areas. Next, the multi-objective genetic algorithm is continued to design initial routes for vehicles between parking points. Finally, the multi-objective genetic algorithm is utilized again to plan delivery routes for customers in no-fly zones, ultimately forming a complete collaborative "vehicle-UAV" delivery scheme.To verify the effectiveness of the model and algorithm, simulation experiments are conducted using two sets of cases: 30 customer points in a local area of Harbin and the large-scale R201 case from the Solomon dataset. The results show that compared with traditional vehicle-only or UAV-only delivery models, the vehicle-UAV collaborative delivery model exhibits significant advantages in total cost, carbon emissions, and customer satisfaction; the model maintains good robustness in stability tests under different no-fly zone settings; and parameter sensitivity analysis further reveals the impact of key parameters (e.g., UAV load capacity, endurance, and vehicle load capacity) on delivery performance, providing practical references for logistics enterprises in equipment selection and operation strategy formulation.