Abstract: To address the problem of time-dependent electric vehicle routing problem (VRP) with drones, this paper comprehensively considers factors such as no-fly zones, simultaneous delivery and pickup, the ability to serve multiple customers in a single drone trip, and the impact of load and speed on energy consumption for both vehicles and drones. To minimize total delivery costs, it develops an optimization model for the electric vehicle routing problem with drones. Given the characteristics of the problem, the initial paths for both vehicles and drones are generated using multi-layer integer coding, and an adaptive large neighborhood search algorithm is designed to solve the model. The algorithm incorporates an operator scoring mechanism to adaptively select removal and insertion operators, along with an inferior solution acceptance criterion form simulated annealing to avoid local optima. The effectiveness of the model and algorithm is demonstrated through several examples, and the impact of factors such as detouring due to no-fly zones, the number of customers served per drone trip, and the lowest state of charge on the delivery scheme is analyzed. The research not only enriches the field of VRP but also expands its scope, providing a theoretical basis for logistics enterprises in optimizing their delivery schemes.

Key words: no-fly zone, time-dependent, electric vehicle-drone cooperative delivery, simultaneous delivery and pickup, adaptive large neighborhood search algorithm

摘要： 针对车辆行驶速度具有时间依赖特性的电动车-无人机协同配送问题，综合考虑分时段禁飞的无人机禁飞区、同时取送货、无人机一次行程可服务多个客户、载重和速度对车辆与无人机能耗的影响等因素，以总配送成本最小化为目标，建立电动车-无人机协同配送优化模型。根据问题特征，采用多层整数编码形式生成车辆、无人机初始路径，设计自适应大邻域搜索算法求解模型，该算法引入算子评分机制对移除、插入算子进行自适应选择，结合模拟退火算法的劣解接受准则，使算法不易陷入局部最优。通过多组算例验证了模型和算法的有效性，并分析了考虑禁飞区绕行、无人机一次行程服务客户数量、最低荷电状态的设置对配送方案的影响。研究成果丰富和拓展了VRP的研究领域，可为物流企业制定配送方案提供理论依据。

关键词: 禁飞区, 时间依赖, 电动车-无人机协同配送, 同时取送货, 自适应大邻域搜索算法