# Deep learning enhanced mixed integer optimization: Learning to reduce model dimensionality

arXiv: https://arxiv.org/abs/2401.09556 · HTML: https://mlsanity.com/paper/2401.09556/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 110 references that are in the map.
- First posted on arXiv 17 Jan 2024.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [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)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems](https://mlsanity.com/paper/1902.01697/) (2019)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Multi-Agent Distributed Optimization via Inexact Consensus ADMM](https://mlsanity.com/paper/1402.6065/) (2014)
- [Deep Learning Assisted Heuristic Tree Search for the Container Pre-marshalling Problem](https://mlsanity.com/paper/1709.09972/) (2017)
- [A Study of Learning Search Approximation in Mixed Integer Branch and Bound: Node Selection in SCIP](https://mlsanity.com/paper/2007.03948/) (2020)
- [Learning to Configure Separators in Branch-and-Cut](https://mlsanity.com/paper/2311.05650/) (2023)
- [Minority Class Oriented Active Learning for Imbalanced Datasets](https://mlsanity.com/paper/2202.00390/) (2022)
- [DOGE-Train: Discrete Optimization on GPU with End-to-end Training](https://mlsanity.com/paper/2205.11638/) (2022)
- [Handling Inter-class and Intra-class Imbalance in Class-imbalanced Learning](https://mlsanity.com/paper/2111.12791/) (2021)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize](https://mlsanity.com/paper/2310.07082/) (2023)
- [Global Optimization: A Machine Learning Approach](https://mlsanity.com/paper/2311.01742/) (2023)
- [A Graph-Based Modeling Abstraction for Optimization: Concepts and Implementation in Plasmo.jl](https://mlsanity.com/paper/2006.05378/) (2020)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part I. Learning when to decompose](https://mlsanity.com/paper/2310.07068/) (2023)
- [An efficient Lagrangian-based heuristic to solve a multi-objective sustainable supply chain problem](https://mlsanity.com/paper/1906.06375/) (2019)
- [Branch-and-Price for a Class of Nonconvex Mixed-Integer Nonlinear Programs](https://mlsanity.com/paper/2001.01794/) (2020)
- [Integrating quantum and classical computing for multi-energy system optimization using Benders decomposition](https://mlsanity.com/paper/2309.16363/) (2023)

## Built on by (most cited first, 1 of 1)

- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)

## Abstract (arXiv)

This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics that identify and exploit common structures across MIP instances. We train deep learning models to estimate complicating binary variables for target MIP problem instances. The resulting reduced MIP models are solved using standard off-the-shelf solvers. We present an algorithm for generating synthetic data enhancing the robustness and generalizability of our models across diverse MIP instances. We compare the effectiveness of (a) feed-forward neural networks (ANN) and (b) convolutional neural networks (CNN). To enhance the framework's performance, we employ Bayesian optimization for hyperparameter tuning, aiming to maximize the occurrence of global optimum solutions. We apply this framework to a flow-based facility location allocation MIP formulation that describes long-term investment planning and medium-term tactical scheduling in a personalized medicine supply chain.