Abstract: Drone delivery has emerged as a significant solution to address the challenges of last-mile logistics. The collaborative delivery model between drones and vehicles overcomes the limitations of insufficient drone delivery capacity and enhances safety, making it a vital approach for drone involvement in the delivery process. To tackle the difficulties and high costs associated with “last-mile” delivery in rural e-commerce logistics, this study constructs a mixed-integer programming model. The objective is to minimize delivery costs while considering constraints such as the collaborative drone-vehicle mode and multi drone multi-parcel delivery. A two-stage algorithm is proposed to optimize the paths for drone-vehicle collaborative delivery. In the first stage, a constrained adaptive K-means algorithm is utilized to determine the range of vehicle docking points. In the second stage, an improved genetic algorithm that incorporates hill climbing and splitting operators is employed to identify the optimal delivery paths for drones and vehicles. Subsequently, a case study experiment is conducted to validate the feasibility and effectiveness of the model and algorithm. The research findings are expected to offer novel insights and valuable references for cost reduction and efficiency improvement in last-mile delivery for rural e-commerce logistics.

Key words: drone and vehicle collaborative delivery, rural logistics, path optimization, two-stage algorithm

摘要： 无人机配送正在成为解决物流末端配送难题的重要手段。无人机与车辆协同配送模式克服了无人机配送能力不足、安全性不高的弊端，是无人机参与配送的重要途径之一。针对农村电商物流“最后一公里”配送难、配送贵问题，考虑无人机与车辆协同方式、多无人机多包裹配送等约束，以配送成本最小化为目标构建混合整数规划模型并提出一种两阶段算法对无人机与车辆协同配送路径优化问题进行求解。第一阶段通过带约束的自适应K-means算法确定车辆停靠点范围，第二阶段设计爬山算子与分裂算子改进遗传算法，求得无人机与车辆配送路径。最后，通过算例实验验证了模型和算法的可行性与有效性。研究成果有望为农村电商物流末端配送降本增效提供新思路和参考价值。

关键词: 无人机与车辆协同配送, 农村电商物流, 路径优化, 两阶段算法