# GREAT: A Graph Edge Attention Network for the Electric Vehicle Routing Problem with Asymmetric Costs

arXiv: https://arxiv.org/abs/2408.16717 · HTML: https://mlsanity.com/paper/2408.16717/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 50 references that are in the map.
- First posted on arXiv 29 Aug 2024.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [An Attention Free Transformer](https://mlsanity.com/paper/2105.14103/) (2021)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)
- [Matrix Encoding Networks for Neural Combinatorial Optimization](https://mlsanity.com/paper/2106.11113/) (2021)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2301.03313/) (2023)
- [Graph Neural Network Guided Local Search for the Traveling Salesperson Problem](https://mlsanity.com/paper/2110.05291/) (2021)
- [Unsupervised Learning for Solving the Travelling Salesman Problem](https://mlsanity.com/paper/2303.10538/) (2023)
- [Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem](https://mlsanity.com/paper/2304.09407/) (2023)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Edgeformers: Graph-Empowered Transformers for Representation Learning on Textual-Edge Networks](https://mlsanity.com/paper/2302.11050/) (2023)
- [Edge-Featured Graph Attention Network](https://mlsanity.com/paper/2101.07671/) (2021)

## Built on by (most cited first, 8 of 8)

- [Learning for routing: A guided review of recent developments and future directions](https://mlsanity.com/paper/2507.00218/) (2025)
- [EFormer: An Effective Edge-based Transformer for Vehicle Routing Problems](https://mlsanity.com/paper/2506.16428/) (2025)
- [Directly Follows Graphs Go Predictive Process Monitoring With Graph Neural Networks](https://mlsanity.com/paper/2503.03197/) (2025)
- [Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs](https://mlsanity.com/paper/2506.22095/) (2025)
- [EGAM: Extended Graph Attention Model for Solving Routing Problems](https://mlsanity.com/paper/2601.21281/) (2026)
- [GREAT-EER: Graph Edge Attention Network for Emergency Evacuation Responses](https://mlsanity.com/paper/2602.14676/) (2026)
- [Two-Stage Learned Decomposition for Scalable Routing on Multigraphs](https://mlsanity.com/paper/2605.05389/) (2026)
- [EDISCO: Equivariant DIScrete Diffusion for Euclidean Combinatorial Optimization](https://mlsanity.com/paper/2610.04953/) (2026)

## Abstract (arXiv)

Due to the ongoing electrification of transportation systems, energy-based routing problems such as the Electric Vehicle Routing Problem (EVRP) are becoming increasingly important. Unlike Euclidean routing problems, the EVRP involves asymmetric energy costs caused by road topology. Existing learning-based routing approaches are based on graph neural networks (GNNs) or transformer architectures operating on Euclidean node coordinates, making them poorly suited for asymmetric, non-Euclidean edge-based metrics such as energy consumption. To address this, we propose the Graph Edge Attention Network (GREAT), a novel GNN-related architecture that operates purely in edge space rather than on node coordinates, making it naturally compatible with asymmetric routing costs. Integrated into an end-to-end reinforcement learning framework, GREAT jointly optimizes routing and charging decisions for the EVRP. We train the model using real-world energy consumption data from San Francisco, derived from physical road networks enriched with topological features, and evaluate generalization on datasets from San Francisco, Vienna, and Gothenburg. Across diverse battery sizes (15-40 kWh) and customer demand distributions, GREAT outperforms a strong HGS-based EVRP heuristic in most tested settings, achieving energy reductions of up to 8.78% while reducing runtime by a factor of 60. Moreover, we benchmark against a custom adaptive large neighborhood search (ALNS) that jointly optimizes routing and charging. GREAT achieves competitive performance at a faster runtime, and we show that the ALNS can profit from a warm start with the GREAT solution. We further evaluate GREAT on standard (asymmetric) routing problems, including Traveling Salesman Problem, Capacitated Vehicle Routing Problem, and Orienteering Problem, where it achieves state-of-the-art performance among neural methods for non-Euclidean settings.