# Analytics and Machine Learning in Vehicle Routing Research

arXiv: https://arxiv.org/abs/2102.10012 · HTML: https://mlsanity.com/paper/2102.10012/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 216 references that are in the map.
- First posted on arXiv 19 Feb 2021.

## Builds on (most cited first, 30 of 34)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [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)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (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)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2004.01608/) (2020)
- [Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1911.04936/) (2019)
- [Learning to Solve NP-Complete Problems - A Graph Neural Network for Decision TSP](https://mlsanity.com/paper/1809.02721/) (2018)
- [A Deep Reinforcement Learning Algorithm Using Dynamic Attention Model for Vehicle Routing Problems](https://mlsanity.com/paper/2002.03282/) (2020)
- [Multi-Vehicle Routing Problems with Soft Time Windows: A Multi-Agent Reinforcement Learning Approach](https://mlsanity.com/paper/2002.05513/) (2020)
- [Revised Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks](https://mlsanity.com/paper/1706.07450/) (2017)
- [On Learning Paradigms for the Travelling Salesman Problem](https://mlsanity.com/paper/1910.07210/) (2019)
- [Learn to Design the Heuristics for Vehicle Routing Problem](https://mlsanity.com/paper/2002.08539/) (2020)
- [Learning the Multiple Traveling Salesmen Problem with Permutation Invariant Pooling Networks](https://mlsanity.com/paper/1803.09621/) (2018)
- [ORL: Reinforcement Learning Benchmarks for Online Stochastic Optimization Problems](https://mlsanity.com/paper/1911.10641/) (2019)
- [A concise guide to existing and emerging vehicle routing problem variants](https://mlsanity.com/paper/1906.06750/) (2019)
- [Robust Optimization using Machine Learning for Uncertainty Sets](https://mlsanity.com/paper/1407.1097/) (2014)
- [Learning-based Robust Optimization: Procedures and Statistical Guarantees](https://mlsanity.com/paper/1704.04342/) (2017)
- [Dynamic Partial Removal: A Neural Network Heuristic for Large Neighborhood Search](https://mlsanity.com/paper/2005.09330/) (2020)
- [Ambulance Emergency Response Optimization in Developing Countries](https://mlsanity.com/paper/1801.05402/) (2018)

## Built on by (most cited first, 22 of 22)

- [Deep Policy Dynamic Programming for Vehicle Routing Problems](https://mlsanity.com/paper/2102.11756/) (2021)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [An Overview and Experimental Study of Learning-based Optimization Algorithms for Vehicle Routing Problem](https://mlsanity.com/paper/2107.07076/) (2021)
- [Generalization in Deep RL for TSP Problems via Equivariance and Local Search](https://mlsanity.com/paper/2110.03595/) (2021)
- [Improving Generalization of Deep Reinforcement Learning-based TSP Solvers](https://mlsanity.com/paper/2110.02843/) (2021)
- [Attention, Filling in The Gaps for Generalization in Routing Problems](https://mlsanity.com/paper/2207.07212/) (2022)
- [Learning for routing: A guided review of recent developments and future directions](https://mlsanity.com/paper/2507.00218/) (2025)
- [Prompt Learning for Generalized Vehicle Routing](https://mlsanity.com/paper/2405.12262/) (2024)
- [Survey on Neural Routing Solvers](https://mlsanity.com/paper/2602.21761/) (2026)
- [Graph Reinforcement Learning for Operator Selection in the ALNS Metaheuristic](https://mlsanity.com/paper/2302.14678/) (2023)
- [Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2503.10421/) (2025)
- [Where the Action is: Let's make Reinforcement Learning for Stochastic Dynamic Vehicle Routing Problems work!](https://mlsanity.com/paper/2103.00507/) (2021)
- [Learning-Enhanced Neighborhood Selection for the Vehicle Routing Problem with Time Windows](https://mlsanity.com/paper/2403.08839/) (2024)
- [GASE: Graph Attention Sampling with Edges Fusion for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2405.12475/) (2024)
- [Project Synapse: A Hierarchical Multi-Agent Framework with Hybrid Memory for Autonomous Resolution of Last-Mile Delivery Disruptions](https://mlsanity.com/paper/2601.08156/) (2026)
- [Combining Constructive and Perturbative Deep Learning Algorithms for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2211.13922/) (2022)
- [Digital Twin Applications in Urban Logistics: An Overview](https://mlsanity.com/paper/2302.00484/) (2023)
- [Pattern based learning and optimisation through pricing for bin packing problem](https://mlsanity.com/paper/2409.04456/) (2024)
- [Data-Driven Stochastic VRP: Integration of Forecast Duration into Optimization for Utility Workforce Management](https://mlsanity.com/paper/2601.07514/) (2026)
- [Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems](https://mlsanity.com/paper/2603.07568/) (2026)
- [Adaptive decision-making for stochastic service network design](https://mlsanity.com/paper/2603.24369/) (2026)
- [Preference-Agile Multi-Objective Optimization for Real-time Vehicle Dispatching](https://mlsanity.com/paper/2604.10664/) (2026)

## Abstract (arXiv)

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in real-world VRP applications, Machine Learning (ML) methods have been used in combination with analytical approaches to enhance problem formulations and algorithmic performance across different problem solving scenarios. However, the relevant papers are scattered in several traditional research fields with very different, sometimes confusing, terminologies. This paper presents a first, comprehensive review of hybrid methods that combine analytical techniques with ML tools in addressing VRP problems. Specifically, we review the emerging research streams on ML-assisted VRP modelling and ML-assisted VRP optimisation. We conclude that ML can be beneficial in enhancing VRP modelling, and improving the performance of algorithms for both online and offline VRP optimisations. Finally, challenges and future opportunities of VRP research are discussed.