A Hybrid Strategy-Assisted Cooperative Vehicles–Drone Multi-Objective Routing Optimization Method for Last-Mile Delivery

Drones have emerged as critical infrastructure for enhancing logistics efficiency in the emerging low-altitude economy, particularly in collaborative vehicle–drone research. However, existing research often neglects the impact of fair task allocation on workload balance among formations in large-scale routing scenarios, which compromises service quality. To address this gap, we introduce the Multi-vehicle with drones Collaborative Routing Problem with Large-scale Packages (MCRPLP), formulated as a bi-objective model aiming to minimize both operational cost and workload imbalance. A Hybrid Strategy-assisted Multi-objective Optimization Algorithm (HSMOA) is developed to overcome the limitations of existing methods, which struggle with balancing solution quality and computational efficiency in solving large-scale routing. Based on a Non-dominated Sorting Genetic Algorithm (NSGA-II), the HSMOA integrates a heuristic task assignment strategy that greedily reassigns packages between adjacent clusters. Then, by integrating a Pareto-front superiority evaluation model, an elite individual supplement strategy is designed to dynamically prune sub-optimal solution subspaces while enhancing the search within high-quality Pareto-front subspaces in HSMOA. Extensive experiments demonstrate the effectiveness of HSMOA in terms of solution quality and computational efficiency compared to multiple state-of-the-art methods. Further sensitivity analysis and managerial insights derived from a real-world case are also provided to support practical logistics implementation.