Token-specific deep reinforcement learning for energy-efficient capacitated electric vehicle routing problems

Nowadays, the electric vehicle routing problem (EVRP) has garnered considerable attention in sustainable energy and transportation research, driven by the environmental promise of electric vehicles (EVs) to reduce carbon emissions and lower energy consumption. However, existing approaches to EVRPs predominantly aim to minimize travel distance, neglecting real-world factors such as road conditions and driving dynamics, which substantially influence the final energy consumption. To bridge this gap, we introduce the energy-efficient capacitated EVRP (CEVRP) and propose an advanced energy consumption model that incorporates practical considerations involving capacity limits, driving resistance, battery efficiency, road characteristics, and vehicle dynamics to capture the multifaceted challenges of EV routing. Building on this foundation, we frame the CEVRP as a customized Markov decision process (MDP) and develop a token-specific deep reinforcement learning (TS-DRL) approach, structured with an encoder–constructor–decoder framework. The encoder disentangles and synthesizes different groups of features for customers and charging stations, generating highly informative node tokens tailored to their unique roles. To adapt to the dynamic nature of CEVRP, the constructor develops a contextual token that integrates real-time EV state information with the active routing sequence, ensuring a comprehensive and continuously updated representation of the environment. Finally, the decoder leverages a compatibility layer to compute probability distributions for node selection, facilitating efficient and precise routing decisions. Extensive experiments conducted on synthetic and real-world datasets demonstrate the effectiveness of our proposed TS-DRL across varying problem sizes and node distributions. The results reveal that TS-DRL consistently outperforms a variety of heuristic and DRL-based methods, achieving energy savings of up to 109.86 kWh (i.e., a reduction of 13.79 %) in scenarios with 100 customers and eight charging stations. These findings highlight the potential of our approach to tackle more complex EV routing challenges in practical energy and transportation systems.