Edge-DIRECT: A Deep Reinforcement Learning-based Method for Solving Heterogeneous Electric Vehicle Routing Problem with Time Window Constraints
Arash Mozhdehi, Mahdi Mohammadizadeh, Xin Wang
TL;DR
This work tackles the heterogeneous electric vehicle routing problem with time-window constraints ($HEVRPTW$), a practical and NP-hard problem in logistics. It introduces Edge-DIRECT, a Transformer-based DRL method with an edge-enhanced encoder and a dual-attention decoder that explicitly models time-window reachability, energy consumption, and fleet heterogeneity. Empirical results on real-world Edmonton and Calgary data show Edge-DIRECT achieving superior solution quality and faster runtimes than state-of-the-art DRL methods and heuristics, especially when using a sampling decoding strategy. The approach advances scalable, energy-aware EV routing by embedding problem structure into a learned policy that can generalize across fleet configurations and time-window scenarios.
Abstract
In response to carbon-neutral policies in developed countries, electric vehicles route optimization has gained importance for logistics companies. With the increasing focus on customer expectations and the shift towards more customer-oriented business models, the integration of delivery time-windows has become essential in logistics operations. Recognizing the critical nature of these developments, this article studies the heterogeneous electric vehicle routing problem with time-window constraints (HEVRPTW). To solve this variant of vehicle routing problem (VRP), we propose a DRL-based approach, named Edge-enhanced Dual attentIon encoderR and feature-EnhanCed dual aTtention decoder (Edge-DIRECT). Edge-DIRECT features an extra graph representation, the node connectivity of which is based on the overlap of customer time-windows. Edge-DIRECT's self-attention encoding mechanism is enhanced by exploiting the energy consumption and travel time between the locations. To effectively account for the heterogeneity of the EVs' fleet, a dual attention decoder has been introduced. Experimental results based on two real-world datasets reveal that Edge-DIRECT outperforms a state-of-the-art DRL-based method and a well-established heuristic approach in solution quality and execution time. Furthermore, it exhibits competitive performance when compared to another leading heuristic method.