To address the limitations of existing vehicle-drone collaborative delivery research, which predominantly focuses on single-objective optimization, employs simple coordination mechanisms, and rarely considers multi-distribution-center scenarios, a multi-objective optimization model for vehicle-drone collaborative delivery with multiple distribution centers is constructed. This model targets the minimization of total transportation cost, total transportation distance, and total transportation time, while respecting constraints including load capacity, drone range, customer time windows, and collaborative synchronization. A computational procedure based on the NSGA-Ⅱ algorithm is developed, which utilizes composite encoding, multi-strategy population initialization, and enhanced genetic operations to improve both the feasibility and diversity of the resulting solutions. Experimental results in a scenario with 4 depots and 36 customers show that the model generates 149 Pareto-optimal solutions, with cost ranging from 7.11 to 23.77 yuan (234.3% variation), distance from 132.52 to 202.56 km (52.9% variation), and time from 137.74 to 393.35 minutes (185.6% 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 35.20 seconds for 96 customers and further to 2560.68 seconds for 396 customers, with solution feasibility improving as scale expands. The Experimental results show that the proposed model and algorithm are feasible and effective, with good adaptability in large-scale application scenarios, and can provide technical support for scientific decision-making in logistics distribution problems.

Aiming at the problems of ignoring road network time-variability, single objective, and insufficient constraint integration in existing vehicle-Unmanned Aerial 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 multiobjective 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 kW·h to 66.67 kW·h. 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.

In urban UAV logistics distribution, the two main components that must be merged are multi-UAV task collaborative allocation and distribution path design. In order to ensure the safety and efficiency of multi-UAV logistics distribution, the grid method is used to model the ultra-low space environment of a three-dimensional city, and the grid risk calculation method is described. Secondly, a two-layer programming model of UAV distribution route and flight path collaborative planning is constructed. In the upper layer model, considering the constraints of UAV load and maximum range, a genetic algorithm is introduced to determine the UAV distribution order with the goal of minimum delay penalty cost. In the lower model, a comprehensive improved particle swarm optimization（CIPSO） algorithm is proposed to solve the flight path of the UAV by considering the performance constraints of the UAV and aiming at the minimization of timeliness cost, UAV height variation, and grid risk. Last but not least, the simulation results demonstrate that CIPSO's overall cost is lower than that of particle swarm optimization（PSO）and improved acceleration coefficients particle swarm optimization（ICPSO）algorithm by 65.00% and 38.41%, respectively. This suggests that the constructed model and the proposed algorithm developed in this study are both practical and efficient.