Route Optimization for Air-Ground Collaborative Delivery with Multiple Distribution Centers

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.