# RouteExplainer: An Explanation Framework for Vehicle Routing Problem

arXiv: https://arxiv.org/abs/2403.03585 · HTML: https://mlsanity.com/paper/2403.03585/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 6 Mar 2024.

## Builds on (most cited first, 22 of 22)

- [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)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Interpretable Explanations of Black Boxes by Meaningful Perturbation](https://mlsanity.com/paper/1704.03296/) (2017)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Role-Play with Large Language Models](https://mlsanity.com/paper/2305.16367/) (2023)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Better Zero-Shot Reasoning with Role-Play Prompting](https://mlsanity.com/paper/2308.07702/) (2023)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Explainable Reinforcement Learning Through a Causal Lens](https://mlsanity.com/paper/1905.10958/) (2019)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [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)
- [Deep Policy Dynamic Programming for Vehicle Routing Problems](https://mlsanity.com/paper/2102.11756/) (2021)
- [Large Language Models are Diverse Role-Players for Summarization Evaluation](https://mlsanity.com/paper/2303.15078/) (2023)
- [ConfusionFlow: A model-agnostic visualization for temporal analysis of classifier confusion](https://mlsanity.com/paper/1910.00969/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [OptiChat: Bridging Optimization Models and Practitioners with Large Language Models](https://mlsanity.com/paper/2501.08406/) (2025)
- [Towards Efficient Constraint Handling in Neural Solvers for Routing Problems](https://mlsanity.com/paper/2602.16012/) (2026)

## Abstract (arXiv)

The Vehicle Routing Problem (VRP) is a widely studied combinatorial optimization problem and has been applied to various practical problems. While the explainability for VRP is significant for improving the reliability and interactivity in practical VRP applications, it remains unexplored. In this paper, we propose RouteExplainer, a post-hoc explanation framework that explains the influence of each edge in a generated route. Our framework realizes this by rethinking a route as the sequence of actions and extending counterfactual explanations based on the action influence model to VRP. To enhance the explanation, we additionally propose an edge classifier that infers the intentions of each edge, a loss function to train the edge classifier, and explanation-text generation by Large Language Models (LLMs). We quantitatively evaluate our edge classifier on four different VRPs. The results demonstrate its rapid computation while maintaining reasonable accuracy, thereby highlighting its potential for deployment in practical applications. Moreover, on the subject of a tourist route, we qualitatively evaluate explanations generated by our framework. This evaluation not only validates our framework but also shows the synergy between explanation frameworks and LLMs. See https://ntt-dkiku.github.io/xai-vrp for our code, datasets, models, and demo.