# Improving Model-based Genetic Programming for Symbolic Regression of Small Expressions

## TL;DR

This paper enhances model-based genetic programming for symbolic regression by improving linkage learning, addressing genotype distribution biases, and demonstrating GOMEA's superior performance on real-world datasets with interpretable small solutions.

## Contribution

The paper introduces a corrected linkage learning method for GOMEA in symbolic regression, improving performance and interpretability over traditional GP.

## Key findings

- GOMEA outperforms traditional and semantic GP in accuracy.
- The new linkage learning method improves model performance.
- Small solutions from GOMEA are competitive with decision trees.

## Abstract

The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a model-based EA framework that has been shown to perform well in several domains, including Genetic Programming (GP). Differently from traditional EAs where variation acts blindly, GOMEA learns a model of interdependencies within the genotype, i.e., the linkage, to estimate what patterns to propagate. In this article, we study the role of Linkage Learning (LL) performed by GOMEA in Symbolic Regression (SR). We show that the non-uniformity in the distribution of the genotype in GP populations negatively biases LL, and propose a method to correct for this. We also propose approaches to improve LL when ephemeral random constants are used. Furthermore, we adapt a scheme of interleaving runs to alleviate the burden of tuning the population size, a crucial parameter for LL, to SR. We run experiments on 10 real-world datasets, enforcing a strict limitation on solution size, to enable interpretability. We find that the new LL method outperforms the standard one, and that GOMEA outperforms both traditional and semantic GP. We also find that the small solutions evolved by GOMEA are competitive with tuned decision trees, making GOMEA a promising new approach to SR.