Drone-vehicle collaborative routing optimization with transfer operations in mountainous environments

To address the core issues of poor vehicle accessibility and insufficient scenario adaptability in logistics systems in mountainous areas and urban fringe environments, a novel collaborative scheduling model for transfer-based drones-vehicle systems is proposed. A freight transportation system consisting of multiple drones carried by mainline distribution vehicles is considered, allowing the simultaneous takeoff of multiple drones from vehicles, where each drone can provide simultaneous pickup and delivery services for one or more customers per flight. The fulfillment of system orders involves three stages: clustering pickup and delivery demands, designing mainline vehicle routes, and determining transfer-based drone routes. Based on the above system, a mixed-integer linear programming model considering time windows and multi-drone-vehicle collaborative operations with transfers is constructed to minimize the total system cost, and an improved artificial bee colony algorithm with cross-neighborhood search is designed to solve large-scale cases. Numerical experiments at different scales were designed based on the high-altitude mountainous areas of Yunnan Province to validate the effectiveness of the model and algorithm. Research results show that, compared with the classical drone-truck parallel collaboration model, the proposed model exhibits superior performance in scenario adaptability and cost efficiency, and reduces costs by 8.0% to 46.7%. Furthermore, the improved artificial bee colony algorithm outperforms the CPLEX solver and other comparative algorithms in both solution efficiency and cost. Particularly for large-scale problems, the solution cost is reduced by 1.4% to 4.3% compared with CPLEX. Finally, sensitivity experiments demonstrate that the model has strong robustness and confirm that adopting a relaxed time window strategy and increasing drone endurance in mountainous environments can effectively improve the efficiency and cost-effectiveness of distribution operations.