M5GP 2.0: Extensions and Enhancements to a Constructive Feature Induction System Based on Genetic Programming

Abstract

Symbolic Regression (SR) aims to discover explicit mathematical expressions that describe the relationship between input variables and a target output, offering an interpretable alternative to black‐box machine learning models. Genetic Programming (GP) has been widely adopted for this purpose; however, traditional GP‐based approaches often suffer from high computational cost, limited scalability, and excessive model complexity. To address these limitations, this work presents M5GP 2.0, an extended version of the Multidimensional Multivariate Genetic Programming framework that builds upon the constructive feature induction paradigm introduced in M5GP (Parallel Multidimensional Genetic Programming with Multidimensional Populations for Symbolic Regression). M5GP 2.0 significantly expands the original framework by extending the evolutionary search space through more expressive and higher‐arity operators and introducing advanced GPU‐based optimisations for efficient large‐scale execution. The proposed method evolves symbolic feature transformations that are subsequently combined using linear models, enabling the generation of compact solutions with interpretability potential while maintaining competitive predictive performance. The experimental evaluation is conducted using a standardised and widely accepted benchmark, namely SRBench, enabling rigorous and reproducible comparisons against state‐of‐the‐art methods considering metrics such as predictive R2$$ {R}^2 $$ , root mean squared error (RMSE), model size, and training time. Overall, the results indicate that M5GP 2.0 constitutes a robust and scalable symbolic regression framework that achieves a favourable balance between predictive performance, model compactness, and computational efficiency, while retaining the potential for symbolic traceability and post hoc interpretability.