# PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs

arXiv: https://arxiv.org/abs/2312.08074 · HTML: https://mlsanity.com/paper/2312.08074/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 13 Dec 2023.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [OMLT: Optimization & Machine Learning Toolkit](https://mlsanity.com/paper/2202.02414/) (2022)
- [Global Deterministic Optimization with Artificial Neural Networks Embedded](https://mlsanity.com/paper/1801.07114/) (2018)
- [ReLU Networks as Surrogate Models in Mixed-Integer Linear Programs](https://mlsanity.com/paper/1907.03140/) (2019)
- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [JANOS: An Integrated Predictive and Prescriptive Modeling Framework](https://mlsanity.com/paper/1911.09461/) (2019)
- [Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded](https://mlsanity.com/paper/1803.00952/) (2018)
- [Boosting Combinatorial Problem Modeling with Machine Learning](https://mlsanity.com/paper/1807.05517/) (2018)
- [Enabling Research through the SCIP Optimization Suite 8.0](https://mlsanity.com/paper/2303.07101/) (2023)
- [ENTMOOT: A Framework for Optimization over Ensemble Tree Models](https://mlsanity.com/paper/2003.04774/) (2020)
- [Between steps: Intermediate relaxations between big-M and convex hull formulations](https://mlsanity.com/paper/2101.12708/) (2021)
- [Augmenting optimization-based molecular design with graph neural networks](https://mlsanity.com/paper/2312.03613/) (2023)
- [Predictive and Prescriptive Analytics for Location Selection of Add-on Retail Products](https://mlsanity.com/paper/1804.01182/) (2018)

## Built on by (most cited first, 8 of 8)

- [Verifying message-passing neural networks via topology-based bounds tightening](https://mlsanity.com/paper/2402.13937/) (2024)
- [Neur2BiLO: Neural Bilevel Optimization](https://mlsanity.com/paper/2402.02552/) (2024)
- [CLCR: Contrastive Learning-based Constraint Reordering for Efficient MILP Solving](https://mlsanity.com/paper/2504.03688/) (2025)
- [MathOptAI.jl: Embed trained machine learning predictors into JuMP models](https://mlsanity.com/paper/2507.03159/) (2025)
- [Relaxation-Informed Training of Neural Network Surrogate Models](https://mlsanity.com/paper/2604.22746/) (2026)
- [Tightening convex relaxations of trained neural networks: a unified approach for convex and S-shaped activations](https://mlsanity.com/paper/2410.23362/) (2024)
- [Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate](https://mlsanity.com/paper/2505.01985/) (2025)
- [DCEmbed: Scalable Optimization over Neural Surrogates](https://mlsanity.com/paper/2609.33879/) (2026)

## Abstract (arXiv)

A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems, information about the relationships between variables is either incomplete or highly complex, making it difficult or even impossible to model the problem directly. To overcome these hurdles, machine learning (ML) predictors are often used to represent these relationships and are then embedded in the MIP as surrogate models. Due to the large amount of available ML frameworks and the complexity of many ML predictors, formulating such predictors into MIPs is a highly non-trivial task. In this paper, we introduce PySCIPOpt-ML, an open-source tool for the automatic formulation and embedding of trained ML predictors into MIPs. By directly interfacing with a broad range of commonly used ML frameworks and an open-source MIP solver, PySCIPOpt-ML provides a way to easily integrate ML constraints into optimisation problems. Alongside PySCIPOpt-ML, we introduce, SurrogateLIB, a library of MIP instances with embedded ML constraints, and present computational results over SurrogateLIB, providing intuition on the scale of ML predictors that can be practically embedded. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.