Drone–Rider Joint Delivery Routing with Arc Obstacle Avoidance

Drone delivery has gained significant traction in e-commerce, particularly for parcel and food delivery. However, existing systems face challenges such as limited delivery range, low efficiency, high costs, and suboptimal customer satisfaction. This paper proposes a novel drone–rider joint delivery model incorporating an Arc Obstacle Avoidance (AOA) strategy to address these issues in complex urban environments. We formulate a multi-objective optimization model aimed at minimizing delivery costs and maximizing customer satisfaction, solved by a Logistic-Logarithmic Dung Beetle Optimization algorithm (LLDBO). Using a modified Solomon dataset and real-world urban simulations in Shenzhen, our experiments demonstrate that the proposed model achieves a 15.3% reduction in delivery costs and a 27.1% increase in delivery efficiency compared to traditional rider-only delivery. Furthermore, customer satisfaction, measured by the on-time delivery rate, shows a 12.4% improvement (from 83.1% to 95.5%) over the rider-only baseline. The AOA strategy also extends the effective delivery range by up to 22.5% compared to conventional linear obstacle avoidance approaches, as measured by the maximum service radius achievable while maintaining 95% on-time delivery performance. These findings validate the practicality and scalability of the proposed approach for real-world last-mile logistics.