# On Statistical Learning of Branch and Bound for Vehicle Routing Optimization

arXiv: https://arxiv.org/abs/2310.09986 · HTML: https://mlsanity.com/paper/2310.09986/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 61 references that are in the map.
- First posted on arXiv 15 Oct 2023.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [Model Similarity Mitigates Test Set Overuse](https://mlsanity.com/paper/1905.12580/) (2019)
- [The advantages of multiple classes for reducing overfitting from test set reuse](https://mlsanity.com/paper/1905.10360/) (2019)

## Abstract (arXiv)

Recently, machine learning of the branch and bound algorithm has shown promise in approximating competent solutions to NP-hard problems. In this paper, we utilize and comprehensively compare the outcomes of three neural networks--graph convolutional neural network (GCNN), GraphSAGE, and graph attention network (GAT)--to solve the capacitated vehicle routing problem. We train these neural networks to emulate the decision-making process of the computationally expensive Strong Branching strategy. The neural networks are trained on six instances with distinct topologies from the CVRPLIB and evaluated on eight additional instances. Moreover, we reduced the minimum number of vehicles required to solve a CVRP instance to a bin-packing problem, which was addressed in a similar manner. Through rigorous experimentation, we found that this approach can match or improve upon the performance of the branch and bound algorithm with the Strong Branching strategy while requiring significantly less computational time. The source code that corresponds to our research findings and methodology is readily accessible and available for reference at the following web address: https://isotlaboratory.github.io/ml4vrp