# Edge-DIRECT: A Deep Reinforcement Learning-based Method for Solving Heterogeneous Electric Vehicle Routing Problem with Time Window Constraints

arXiv: https://arxiv.org/abs/2407.01615 · HTML: https://mlsanity.com/paper/2407.01615/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 28 Jun 2024.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Self-critical Sequence Training for Image Captioning](https://mlsanity.com/paper/1612.00563/) (2016)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Deep Reinforcement Learning for Multi-objective Optimization](https://mlsanity.com/paper/1906.02386/) (2019)
- [Heterogeneous Attentions for Solving Pickup and Delivery Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2110.02634/) (2021)
- [Graph Neural Networks with Adaptive Readouts](https://mlsanity.com/paper/2211.04952/) (2022)
- [Deep Reinforcement Learning for Electric Vehicle Routing Problem with Time Windows](https://mlsanity.com/paper/2010.02068/) (2020)

## Built on by (most cited first, 2 of 2)

- [Learning to Search for Vehicle Routing with Multiple Time Windows](https://mlsanity.com/paper/2505.23098/) (2025)
- [GAMA: A Neural Neighborhood Search Method with Graph-aware Multi-modal Attention for Vehicle Routing Problem](https://mlsanity.com/paper/2511.07850/) (2025)

## Abstract (arXiv)

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.