Balancing Efficiency and Sustainability in Last-Mile Logistics: A Novel Multi-Truck Multi-Drone Collaborative Framework with Bi-Objective Optimization

The increasing variety in last-mile delivery demands requires diverse vehicle-drone collaboration models to meet various scenarios. Meanwhile, growing environmental concerns demand that we optimize not just delivery efficiency but also sustainability. This study thus proposes a unified multi-mode framework for collaborative multi-vehicle, multi-drone delivery networks to enable fair model comparisons. We introduce a hybrid metaheuristic algorithm combining NSGA-II and VND using specialized encoding and neighborhood structures to handle complex constraints, thereby comprehensively enhancing both efficiency and sustainability. Experiments on nine benchmark instances across three models reveal a nonlinear trade-off between efficiency and sustainability, with our migratory-relay model consistently outperforming others in terms of the Pareto front across multiple comparisons. Sensitivity analysis shows diminishing returns from adding more drones; while the first drone can cut emissions by up to 23.1%, additional drones bring progressively smaller reductions. These findings provide a strong framework and practical insights for designing sustainable urban logistics systems.