Shapiro-Wilk test results.

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.

随着电子商务的快速发展，物流配送系统面临着效率提升与成本控制的双重压力。无人机（Unmanned Aerial Vehicle, UAV）配送凭借灵活性高、效率出众、低碳排放的特性，成为解决“最后一公里”配送难题的有效手段。然而，城市环境中广泛分布的禁飞区（如机场、政府机构、高压输电线路）严重限制了无人机的应用范围，同时增加了路径规划的复杂度。在此背景下，车辅无人机协同配送模式应运而生：通过地面车辆与无人机的分工协作，既拓展了无人机的服务半径，又突破了禁飞区的约束，实现了配送效率与服务质量的双重提升。本研究聚焦于禁飞区约束下车辅无人机配送路径的优化问题，旨在构建兼顾配送成本、碳排放与客户满意度的多目标优化模型，并设计高效的求解算法，为物流企业提供科学的决策支持。首先，本文系统梳理了禁飞区的分类、定义及其对无人机路径规划的影响机制，并详细阐述了车-无人机协同配送的理论基础，包括问题的构成要素、客户满意度量化方法以及启发式算法的应用框架。在此基础上，以总配送成本最小化、碳排放最小化与客户满意度最大化为目标，构建了混合整数规划模型。鉴于该模型属于NP难（NP-hard）问题范畴，本文设计了四阶段启发式求解方法：第一阶段，采用改进K-means算法（Improved K-means, IKM）在无人机最大飞行半径约束下对客户点进行聚类，以确定车辆停靠点；第二阶段，运用多目标遗传算法为开放区域内的客户规划无人机配送路径；第三阶段，继续通过多目标遗传算法为车辆在停靠点间规划初始配送路径；第四阶段，再次利用多目标遗传算法为禁飞区内的客户规划配送路径，最终形成完整的“车-无人机”协同配送方案。为验证模型与算法的有效性，本文采用两组案例开展仿真实验：哈尔滨局部区域的30个客户点，以及所罗门（Solomon）数据集的大规模R201案例。实验结果表明，相较于传统的纯车辆配送或纯无人机配送模式，车-无人机协同配送模型在总成本、碳排放与客户满意度方面均具备显著优势；在不同禁飞区设置下的稳定性测试中，该模型保持了良好的鲁棒性；参数敏感性分析进一步揭示了无人机载荷能力、续航能力以及车辆载荷能力等关键参数对配送绩效的影响，可为物流企业的设备选型与运营策略制定提供实践参考。