Optimizing routing for autonomous delivery and pickup vehicles in three-dimensional space

The last-mile delivery challenge in three-dimensional (3D) multi-floor building environments has a significant impact on logistics efficiency. Although autonomous delivery robots (ADRs) have been widely adopted to address last-mile logistics, most existing studies focus on optimizing ADR routing in simplified two-dimensional environments. Moreover, optimal layout of goods within the robot's physical containers brings another challenge. Hence, this paper formalizes the Discrete Capacity Vehicle Routing Problem with Simultaneous Delivery-Pickup and Soft Time Windows (DCVRP-SDP-STW) in a 3D environment. To achieve high-quality solutions, we propose an improved ant colony optimization algorithm that considers spatiotemporal multi-stage clustering characteristics, leading to a significant reduction in computation time. A data preprocessing framework is also developed to convert real-world architectural topologies into navigable 3D routing networks. To validate the proposed model and algorithm, we conducted a case study in Nanjing. The results show that the algorithm can improve optimization outcomes by 23% to 94% compared to pre-optimization results based on the proximity principle, which can contribute to the advancement of efficient and intelligent autonomous delivery systems.