# Reinforcement Learning for Efficient Drone-Assisted Vehicle Routing
## 6 Conclusions  
In this study, the main focus was on learning and coordinating multiple vehicles with multiple drones to optimize routing dynamics in scenarios involving both vehicles and drones. The exploration and evaluation, especially when testing the model on large and small instances using well-known benchmarks, provided valuable insights into its adaptability and efficiency.  
The study, centred around various configurations manipulating factors like drone flight range, the number of vehicles, and drone allocations, consistently demonstrated the comparable performance of RL approaches with traditional methods. Notably, it demonstrated adaptability in scenarios with limited drone flight range, delivering solutions that balance quality and computational speed.  
The findings reinforce that the RL model holds significant promise for addressing challenges and optimizing efficiency in drone-assisted vehicle routing. Further exploration of this model, particularly in scenarios involving an increased number of vehicles and drones, presents exciting opportunities to enhance its optimality and robustness in real-world logistics applications.  
Additionally, exploring scenarios with an increased number of nodes could provide valuable insights and contribute to the continued advancement of this research field. In  
Figure 2: Drones’ and trucks’ routes produced by the RL sampling approach with \(\beta=0.6\) on a graph with 10 nodes. The solid lines in black and blue colors correspond to the first and second truck’s routes, and the dashed lines correspond to their assigned drones’ routes.  
conclusion, this research suggests that RL-based models are valuable for planning routes involving vehicles and drones. Exploring its capabilities more thoroughly, the promising potential is seen to improve how deliveries are managed in the future.  
Despite these promising directions, the current study has certain limitations that warrant further investigation. First, complex recharging or maintenance schedules for drones are not explicitly modeled, which may limit the applicability of the approach in extended delivery routes or highly variable environments. Second, although strong adaptability is demonstrated by the proposed model in benchmark settings, the robustness would be better validated through additional testing with real-world datasets and unpredictable factors (e.g., weather conditions and traffic disruptions). Finally, while multiple drones and vehicles are considered, exploring larger-scale deployments and more intricate constraints (e.g., multi-objective objectives balancing cost, time, and environmental impact) could uncover new challenges and optimization opportunities. Future work could address these aspects by integrating dynamic recharging strategies, employing real-time data streams for adaptive routing, and evaluating the performance across a broader range of industrial and urban scenarios. It is believed that the proposed reinforcement learning framework can evolve into a fully operational tool for last-mile logistics and beyond by being implemented.  
Conceptualization, B.D. and M.M.; methodology, A.B.; software, B.D.; validation, M.M. and A.B.; formal analysis, M.M.; investigation, A.B.; resources, A.B.; data curation, B.D.; writing--original draft preparation, B.D.; writing--review and editing, A.B.; visualization, M.M.; supervision, A.B.; project administration, M.M.; funding acquisition, A.B. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Ministry of Science and Higher Education of the Republic of Kazakhstan, IRN AP19575607.  
Not applicable.  
Data Availability Statement: Data is available upon a request from the authors.  
The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.