# Complexity Measures for Multi-objective Symbolic Regression

arXiv: https://arxiv.org/abs/2109.00238 · HTML: https://mlsanity.com/paper/2109.00238/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 15 references that are in the map.
- First posted on arXiv 1 Sep 2021.

## Built on by (most cited first, 11 of 11)

- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Controllable Neural Symbolic Regression](https://mlsanity.com/paper/2304.10336/) (2023)
- [Priors for symbolic regression](https://mlsanity.com/paper/2304.06333/) (2023)
- [Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition](https://mlsanity.com/paper/2304.01117/) (2023)
- [Introducing Thermodynamics-Informed Symbolic Regression -- A Tool for Thermodynamic Equations of State Development](https://mlsanity.com/paper/2309.02805/) (2023)
- [rEGGression: an Interactive and Agnostic Tool for the Exploration of Symbolic Regression Models](https://mlsanity.com/paper/2501.17859/) (2025)
- [Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations](https://mlsanity.com/paper/2404.09788/) (2024)
- [MOT-SR: Multi-Objective Tool-Augmented Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2607.29561/) (2026)
- [Decision-Making under Combinatorial Risk](https://mlsanity.com/paper/2606.10092/) (2026)
- [LLMs as Post-hoc Auditors of Physiological Plausibility in Symbolic Regression: A Clinician-Evaluated Case Study](https://mlsanity.com/paper/2609.11431/) (2026)

## Abstract (arXiv)

Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity. In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi- objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected.