Routing optimization for an eVTOL-and-drone delivery system in continuous space with no-fly zones: A reinforcement learning approach

The integration of electric vertical takeoff and landing (eVTOL) vehicles and drones offers a promising solution for time-sensitive last-mile delivery in urban environments. This paper studies a novel routing optimization problem in a continuous 2D space, where an eVTOL mothership carries multiple drones to deliver parcels. The challenge lies in optimizing the mothership’s trajectory to coordinate drone dispatch and retrieval efficiently, while avoiding designated no-fly zones that may represent regulatory or physical obstacles for large eVTOL. We formulate the problem as mixed-integer second-order cone programming (MISOCP) models over discrete time and continuous space, with the objective of minimizing the overall delivery makespan-that is, the time at which all parcels have been delivered and all drones have been retrieved by the eVTOL. Given the high computational burden of solving the MISOCP models, we develop a reinforcement learning (RL) framework to learn effective routing policies. Since the eVTOL trajectory admits multiple solutions under the minimal makespan, a visibility-graph-based post-processing method is introduced to refine the eVTOL path while respecting no-fly zone constraints. Experimental results demonstrate that the proposed RL method achieves effective coordination between the eVTOL and its drones, and significantly outperforms baseline methods in environments with complex obstacle configurations.