College of Air traffic Management, Civil Aviation University of China, Tianjin 300300, China

针对现有车辆—无人机协同配送研究中单目标优化为主、协同机制简单及多配送中心场景较少等问题，本文构建多配送中心的车辆—无人机协同配送多目标优化模型。该模型以总运输成本、总运输距离及总运输时间最小化为目标，以载重限制、无人机航程、客户时间窗和协同同步等约束条件；设计基于 NSGA-II 算法的求解算例，通过复合编码、多策略种群初始化及改进遗传操作提升解的可行性与多样性。算例验证表明，模型在含4个配送中心、36个客户的场景中可生成149个帕累托前沿解，其中配送费用范围为4.69-29.04 元，变化幅度达518.9%；配送距离为148.48-202.56km，变化幅度为36.4%；配送时间为136.07-503.07分钟，变化幅度达269.6%，实现了多目标间的有效权衡。在36至396个客户规模下均能高效输出可行解，其中36个客户场景计算时间仅189.99秒，96个客户场景计算时间增至335.20秒，396个客户场景计算时间为2560.68秒，且可行解生成率随规模扩大逐步提升。实验结果说明，本文的模型与算法是可行和有效的，在大规模应用场景下具有良好适应性，能够为物流配送问题的科学决策提供技术支撑。

Existing research on vehicle-drone collaborative delivery often focuses on single-objective optimization, employs simplistic coordination mechanisms, and seldom considers multi-depot scenarios. To address these limitations, this paper develops a multi-objective optimization model for multi-depot vehicle-drone collaborative delivery. The model aims to minimize total cost, distance, and time, subject to constraints such as load capacity, drone range, time windows, and synchronization requirements.

A solution approach based on the NSGA-II algorithm is designed, incorporating composite encoding, multi-strategy population initialization, and improved genetic operations to enhance solution feasibility and diversity. Experimental results in a scenario with 4 depots and 36 customers show that the model generates 149 Pareto-optimal solutions, with cost ranging from 4.69 to 29.04 yuan (518.9% variation), distance from 148.48 to 202.56 km (36.4% variation), and time from 136.07 to 503.07 minutes (269.6% variation), demonstrating effective trade-offs among objectives.

The method efficiently produces feasible solutions across scales of 36 to 396 customers. Computation time increases from 189.99 seconds for 36 customers to 2560.68 seconds for 396 customers, with solution feasibility improving as scale expands. The results confirm the feasibility, effectiveness, and scalability of the proposed model and algorithm, supporting decision-making in logistics optimization.