# Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decompose

arXiv: https://arxiv.org/abs/2310.07068 · HTML: https://mlsanity.com/paper/2310.07068/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 65 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 15 of 15)

- [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)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Automated Algorithm Selection: Survey and Perspectives](https://mlsanity.com/paper/1811.11597/) (2018)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Understanding Pooling in Graph Neural Networks](https://mlsanity.com/paper/2110.05292/) (2021)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Lagrangian Decomposition for Neural Network Verification](https://mlsanity.com/paper/2002.10410/) (2020)
- [Lookback for Learning to Branch](https://mlsanity.com/paper/2206.14987/) (2022)
- [Learning to Reformulate for Linear Programming](https://mlsanity.com/paper/2201.06216/) (2022)

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

- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality](https://mlsanity.com/paper/2401.09556/) (2024)
- [Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering](https://mlsanity.com/paper/2610.02014/) (2026)

## Abstract (arXiv)

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures the structural and functional coupling among the variables and constraints of the problem via an appropriate set of features. Given this representation, a graph classifier is built to determine the best solution method for a given problem. The proposed approach is used to develop a classifier that determines whether a convex Mixed Integer Nonlinear Programming problem should be solved using branch and bound or the outer approximation algorithm. Finally, it is shown how the learned classifier can be incorporated into existing mixed integer optimization solvers.