A transformer-based deep reinforcement learning for the Dial-a-Ride problem

Dial-a-Ride problem (DARP) is a specialized variant of the vehicle routing problem that focuses on designing optimal routes for users who specify pick-up and delivery requests between origins and destinations. This problem involves determining the most effective and efficient routes using limited vehicles and resources to offer responsive door-to-door transportation services for users with specific needs. Logistics service providers require systems that can deliver optimal solutions to these combinatorial problems within a reasonable time. Recently, there has been a significant increase in the use of artificial intelligence optimization algorithms such as meta-heuristics or learning-based approaches to solve such problems. Among the learning-based approaches, reinforcement learning has gained prominence for routing and scheduling tasks, owing to its ability to adaptively learn from complex state spaces and dynamically changing environments. In this study, a novel transformer-based deep reinforcement learning method is proposed to solve the Dial and Ride problem for a single service vehicle. In the proposed model, we adopt a modified transformer architecture instead of employing traditional linear layers, we integrate convolutional layers. To validate our approach, we conduct comprehensive experiments comparing our method against four well-known metaheuristic algorithms and a Deep Q-Network algorithm. The results indicate that proposed approach outperforms these techniques in terms of shorter total travel distances. Additionally, the proposed method is tested on a real-world scenario generated in the Buyukdere neighborhood of Eskisehir. The results demonstrate that the proposed method makes it possible to solve the problem within a reasonable time. This study confirms that the proposed deep reinforcement learning method can effectively address the Dial-a-Ride Problems. © The Author(s) 2025.