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

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.

arXiv commentfix NMSE definition (it is 100xMSE/var instead of MSE/var)

References in corpus (5)

• XGBoost: A Scalable Tree Boosting System
• Where are we now? A large benchmark study of recent symbolic regression methods
• Optimization by Pairwise Linkage Detection, Incremental Linkage Set, and Restricted / Back Mixing: DSMGA-II
• Solving the Exponential Growth of Symbolic Regression Trees in Geometric Semantic Genetic Programming
• Symbolic Regression Algorithms with Built-in Linear Regression

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