# OMLT: Optimization & Machine Learning Toolkit

arXiv: https://arxiv.org/abs/2202.02414 · HTML: https://mlsanity.com/paper/2202.02414/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 37 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Meta-Learning Acquisition Functions for Transfer Learning in Bayesian Optimization](https://mlsanity.com/paper/1904.02642/) (2019)
- [Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming](https://mlsanity.com/paper/2010.11645/) (2020)
- [The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification](https://mlsanity.com/paper/2006.14076/) (2020)
- [Partition-based formulations for mixed-integer optimization of trained ReLU neural networks](https://mlsanity.com/paper/2102.04373/) (2021)
- [Lossless Compression of Deep Neural Networks](https://mlsanity.com/paper/2001.00218/) (2020)
- [Global Deterministic Optimization with Artificial Neural Networks Embedded](https://mlsanity.com/paper/1801.07114/) (2018)
- [JANOS: An Integrated Predictive and Prescriptive Modeling Framework](https://mlsanity.com/paper/1911.09461/) (2019)
- [Optimization of Tree Ensembles](https://mlsanity.com/paper/1705.10883/) (2017)
- [The ALAMO approach to machine learning](https://mlsanity.com/paper/1705.10918/) (2017)
- [Maximizing information from chemical engineering data sets: Applications to machine learning](https://mlsanity.com/paper/2201.10035/) (2022)
- [Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded](https://mlsanity.com/paper/1803.00952/) (2018)
- [ENTMOOT: A Framework for Optimization over Ensemble Tree Models](https://mlsanity.com/paper/2003.04774/) (2020)
- [Multi-Objective Constrained Optimization for Energy Applications via Tree Ensembles](https://mlsanity.com/paper/2111.03140/) (2021)
- [Between steps: Intermediate relaxations between big-M and convex hull formulations](https://mlsanity.com/paper/2101.12708/) (2021)
- [Modeling Design and Control Problems Involving Neural Network Surrogates](https://mlsanity.com/paper/2111.10489/) (2021)

## Built on by (most cited first, 30 of 35)

- [When Deep Learning Meets Polyhedral Theory: A Survey](https://mlsanity.com/paper/2305.00241/) (2023)
- [Physics-Informed Neural Networks with Hard Linear Equality Constraints](https://mlsanity.com/paper/2402.07251/) (2024)
- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spaces](https://mlsanity.com/paper/2207.00879/) (2022)
- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [Verifying message-passing neural networks via topology-based bounds tightening](https://mlsanity.com/paper/2402.13937/) (2024)
- [PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs](https://mlsanity.com/paper/2312.08074/) (2023)
- [P-split formulations: A class of intermediate formulations between big-M and convex hull for disjunctive constraints](https://mlsanity.com/paper/2202.05198/) (2022)
- [Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks](https://mlsanity.com/paper/2312.16699/) (2023)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)
- [Reinforcement learning with combinatorial actions for coupled restless bandits](https://mlsanity.com/paper/2503.01919/) (2025)
- [Molecular Machine Learning in Chemical Process Design](https://mlsanity.com/paper/2508.20527/) (2025)
- [Data-driven decision-focused surrogate modeling](https://mlsanity.com/paper/2308.12161/) (2023)
- [Global Optimization: A Machine Learning Approach](https://mlsanity.com/paper/2311.01742/) (2023)
- [A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equations](https://mlsanity.com/paper/2504.04665/) (2025)
- [Training Neural ODEs Using Fully Discretized Simultaneous Optimization](https://mlsanity.com/paper/2502.15642/) (2025)
- [Model-based feature selection for neural networks: A mixed-integer programming approach](https://mlsanity.com/paper/2302.10344/) (2023)
- [A Constraint Enforcement Deep Reinforcement Learning Framework for Optimal Energy Storage Systems Dispatch](https://mlsanity.com/paper/2307.14304/) (2023)
- [Survey and Tutorial of Reinforcement Learning Methods in Process Systems Engineering](https://mlsanity.com/paper/2510.24272/) (2025)
- [Relaxation-Informed Training of Neural Network Surrogate Models](https://mlsanity.com/paper/2604.22746/) (2026)
- [Physics Informed Piecewise Linear Neural Networks for Process Optimization](https://mlsanity.com/paper/2302.00990/) (2023)
- [LEVIS: Large Exact Verifiable Input Spaces for Neural Networks](https://mlsanity.com/paper/2408.08824/) (2024)
- [Formulations and scalability of neural network surrogates in nonlinear optimization problems](https://mlsanity.com/paper/2412.11403/) (2024)
- [Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees](https://mlsanity.com/paper/2506.03531/) (2025)
- [Nonlinear Optimization with GPU-Accelerated Neural Network Constraints](https://mlsanity.com/paper/2509.22462/) (2025)
- [Optimizing the switching operation in monoclonal antibody production: Economic MPC and reinforcement learning](https://mlsanity.com/paper/2308.03928/) (2023)
- [Optimization over Trained (and Sparse) Neural Networks: A Surrogate within a Surrogate](https://mlsanity.com/paper/2505.01985/) (2025)
- [Neural Two-Stage Stochastic Optimization for Solving Unit Commitment Problem](https://mlsanity.com/paper/2507.09503/) (2025)
- [Convex Hybrid Modeling: An Operator-Based Approach](https://mlsanity.com/paper/2605.23151/) (2026)
- [Generative Robust Optimisation](https://mlsanity.com/paper/2606.22536/) (2026)

## Abstract (arXiv)

The optimization and machine learning toolkit (OMLT) is an open-source software package incorporating neural network and gradient-boosted tree surrogate models, which have been trained using machine learning, into larger optimization problems. We discuss the advances in optimization technology that made OMLT possible and show how OMLT seamlessly integrates with the algebraic modeling language Pyomo. We demonstrate how to use OMLT for solving decision-making problems in both computer science and engineering.