# Data-driven Mixed Integer Optimization through Probabilistic Multi-variable Branching

arXiv: https://arxiv.org/abs/2305.12352 · HTML: https://mlsanity.com/paper/2305.12352/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 21 May 2023.

## Builds on (most cited first, 18 of 18)

- [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)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies](https://mlsanity.com/paper/2002.05120/) (2020)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (2022)
- [Learning to branch with Tree MDPs](https://mlsanity.com/paper/2205.11107/) (2022)
- [Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs](https://mlsanity.com/paper/2107.10201/) (2021)
- [A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2302.05636/) (2023)
- [Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems](https://mlsanity.com/paper/1902.01697/) (2019)
- [Learning Large Neighborhood Search Policy for Integer Programming](https://mlsanity.com/paper/2111.03466/) (2021)
- [Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts](https://mlsanity.com/paper/2204.07312/) (2022)
- [Cardinal Optimizer (COPT) User Guide](https://mlsanity.com/paper/2208.14314/) (2022)
- [An Improved Reinforcement Learning Algorithm for Learning to Branch](https://mlsanity.com/paper/2201.06213/) (2022)
- [Improved Sample Complexity Bounds for Branch-and-Cut](https://mlsanity.com/paper/2111.11207/) (2021)
- [Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs](https://mlsanity.com/paper/1604.08448/) (2016)
- [Expected Performance and Worst Case Scenario Analysis of the Divide-and-Conquer Method for the 0-1 Knapsack Problem](https://mlsanity.com/paper/2008.04124/) (2020)

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

- [FMIP: Joint Continuous-Integer Flow For Mixed-Integer Linear Programming](https://mlsanity.com/paper/2507.23390/) (2025)

## Abstract (arXiv)

In this paper, we propose a Pre-trained Mixed Integer Optimization framework (PreMIO) that accelerates online mixed integer program (MIP) solving with offline datasets and machine learning models. Our method is based on a data-driven multi-variable cardinality branching procedure that splits the MIP feasible region using hyperplanes chosen by the concentration inequalities. Unlike most previous ML+MIP approaches that either require complicated implementation or suffer from a lack of theoretical justification, our method is simple, flexible, provable, and explainable. Numerical experiments on both classical OR benchmark datasets and real-life instances validate the efficiency of our proposed method.