Abstract: Aiming at the problems of ignoring road network time-variability, single objective, and insufficient constraint integration in existing vehicle-UAV collaborative delivery research, this study focuses on the scenario of pickup and delivery with multiple distribution centers. Taking "minimizing total path length, minimizing penalty cost, and minimizing total energy consumption" as the decision-making objectives, it integrates multiple constraints such as time-varying speed, soft time windows, UAV endurance, and load capacity. A time-varying speed model based on time segment division and a penalty mechanism for soft time windows are proposed, and a multi-objective and multi-constraint optimization model is constructed. On the basis of NSGA-II, a three-layer chromosome coding structure of "customer sequencing - distribution center allocation - UAV service marking" is designed. This structure is combined with a hybrid crossover operator, three types of mutation operators (crossover mutation, single-point mutation, and bit-flipping mutation), and a two-layer selection strategy (tournament selection and elitism preservation), thus establishing an improved NSGA-II algorithm to solve the model. A case study is carried out based on 4 distribution centers and 36 customers. The results show that the total path length of the improved NSGA-II algorithm ranges from 100.35 km to 291.21 km, the penalty cost ranges from 831.69 yuan to 12,323.58 yuan, and the total energy consumption ranges from 20.88 kWh to 66.67 kWh. The generated Pareto frontier has a uniform distribution, and its comprehensive performance in terms of HV, IGD, and Spacing indicators is significantly better than that of other multi-objective algorithms such as SPEA2, MOEA/D, and NSGA-III. Furthermore, verification is conducted using the real road network of some main urban areas in Tianjin as the scenario. Actual road distance data are obtained by integrating the Amap API, and a delivery network with multi-type customer demands under a real city environment is constructed. The results indicate that the optimized scheme can adapt to the characteristics of complex urban road networks and heterogeneous demands, while balancing the objectives of efficiency, cost, and low carbon. The study confirms that the constructed model and algorithm are feasible and effective, and can provide decision support for logistics enterprises that is consistent with practical scenarios.

Key words: Low-altitude economy, Vehicle-drone collaborative delivery, Task assignment, Time-varying network, Soft time window, Multi-objective optimization, NSGA-II