Heterogeneous attention-driven deep reinforcement learning for solving EVRPs with pickup-delivery and time windows

Electric vehicle routing problems (EVRPs) have attracted growing interest in the pursuit of sustainable transportation, driven by the environmental benefits and energy efficiency of electric vehicles (EVs). Nevertheless, mainstream approaches predominantly focus on minimizing travel distance rather than propulsion energy and overlook key logistical constraints such as time windows and pickup-delivery demands, which are critical in modern express operations. To address these limitations, we investigate an energy-optimal EVRP with pickup-delivery and time windows (EVRP-PDTW) and develop a high-resolution energy consumption model that integrates time-dependent driving dynamics, detailed road information, and battery charging behavior. Building on this foundation, we cast the routing task as a Markov decision process and propose a Heterogeneous Attention-driven Deep Reinforcement Learning (HA-DRL) framework. The encoder leverages a heterogeneous attention mechanism to capture role-specific interactions among depots, customers, and charging stations, while the decoder incorporates a dynamic-aware context embedding to capture state transitions and temporal feasibility. We analyze how these design choices structure the decision space and align the learned policy with the underlying energy model, thereby explaining the observed energy savings. Experiments on synthetic and real-world datasets show that HA-DRL outperforms a suite of heuristic and DRL-based methods by a clear margin, reducing average energy consumption by 51.30 kWh (a 6.43% improvement in optimality gap) over the competitive NCS approach in large-scale scenarios involving 200 customers and 40 charging stations. These achievements underscore the promise of HA-DRL in advancing energy-aware routing solutions for real-world EV logistics systems.