Node Importance-Based Multi-Objective Genetic Programming for Enhanced Model Interpretability in Symbolic Regression

Interpretability is a critical requirement in high-stakes real-world applications. Genetic Programming (GP) is one of the most interpretable machine learning algorithms currently available. While certain datasets necessitate complex GP models to capture underlying patterns, others may not require such complexity. However, GP lacks a mechanism to dynamically assess the required model complexity during evolution. As a result, GP often evolves overly complex models that are challenging to analyze, thereby reducing interpretability. This paper introduces a novel algorithm designed to evolve compact multi-objective GP models without significantly compromising regression error, thereby enhancing interpretability. The proposed method employs NSGA-II to simultaneously minimize regression error and maximize a newly introduced per-node importance metric. This metric quantifies the contribution of each node in terms of error reduction. By leveraging this metric, the algorithm discards large GP models containing many low-importance nodes, effectively avoiding unnecessarily complex solutions. Experimental results on ten regression datasets demonstrate that the proposed method consistently evolves smaller GP models with better interpretability while maintaining competitive predictive performance, particularly on high-dimensional datasets.