# Symbolic Regression using Mixed-Integer Nonlinear Optimization

arXiv: https://arxiv.org/abs/2006.06813 · HTML: https://mlsanity.com/paper/2006.06813/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 5 of 5)

- [In Context Learning and Reasoning for Symbolic Regression with Large Language Models](https://mlsanity.com/paper/2410.17448/) (2024)
- [Taming Binarized Neural Networks and Mixed-Integer Programs](https://mlsanity.com/paper/2310.04469/) (2023)
- [Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics](https://mlsanity.com/paper/2102.08351/) (2021)
- [Symbolic Density Estimation for Discrete Distributions](https://mlsanity.com/paper/2605.21813/) (2026)
- [Trustworthy Machine Learning through the Lens of Combinatorial Optimization: Survey and Research Perspectives](https://mlsanity.com/paper/2607.07762/) (2026)

## Abstract (arXiv)

The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both theoretically and computationally. Genetic programming based methods, that heuristically search over a very large space of functions, are the most commonly used methods to tackle SR problems. An alternative mathematical programming approach, proposed in the last decade, is to express the optimal symbolic expression as the solution of a system of nonlinear equations over continuous and discrete variables that minimizes a certain objective, and to solve this system via a global solver for mixed-integer nonlinear programming problems. Algorithms based on the latter approach are often very slow. We propose a hybrid algorithm that combines mixed-integer nonlinear optimization with explicit enumeration and incorporates constraints from dimensional analysis. We show that our algorithm is competitive, for some synthetic data sets, with a state-of-the-art SR software and a recent physics-inspired method called AI Feynman.