Autonomous delivery vehicle routing problem with drones based on multiple delivery modes

Abstract

Autonomous delivery vehicles (ADVs) and drones have gained widespread attention in the last-mile delivery due to their efficiency, environmental sustainability, and convenience. Moreover, the cooperative delivery between ADVs and drones is very complex, and most of the existing studies are focused on the cooperative delivery between trucks and drones in a single delivery mode. In contrast, this paper introduces a new vehicle routing problem for an unmanned delivery system consisting of ADVs and heterogeneous drones based on multiple delivery modes. A mixed integer programming (MIP) model is constructed for the autonomous delivery vehicle routing problem with drones based on multiple delivery modes (ADVRPD-MDM) with the objective of minimizing cost. We design a randomized variable neighborhood search (RVNS) algorithm that incorporates 12 specific neighborhood structures, a random variable neighborhood descent (RVND) mechanism and a random shaking strategy to solve the model. We evaluate the application effects of each operator and verify the effectiveness of the RVNS algorithm by the improved Solomon instances. Furthermore, when compared to the large neighborhood search (LNS) algorithm in 56 instances, the RVNS algorithm demonstrates an average improvement of 3.86% in its lowest solution, thereby confirming its superior performance. Through a series of experiments, it has been observed that the integration of collaborative drones and parallel drones within the unmanned delivery system can effectively reduce the cost. The results of the sensitivity analysis demonstrate that factors such as the multi-visit capability, the utilization of multiple drones, the high payload capacity, the long endurance, and the rapid charging rate are critical in reducing the cost. Finally, we verify through a case study that the unmanned delivery system with the ADV as carrier offers cost advantages compared to those employing trucks.