Coefficient Mutation in the Gene-pool Optimal Mixing Evolutionary Algorithm for Symbolic Regression

TL;DR

This paper enhances the GP-GOMEA algorithm for symbolic regression by integrating simple coefficient mutation methods, demonstrating improved ability to rediscover underlying equations in noise-free data and maintaining accuracy with noisy data.

Contribution

It introduces and evaluates Gaussian coefficient mutation variants within GP-GOMEA, showing how to effectively optimize coefficients during symbolic regression.

Findings

Coefficient mutation improves equation discovery in noise-free data.

Number of mutation attempts correlates with mixing operations for effectiveness.

Coefficient mutation maintains accuracy in noisy data, discovering alternative solutions.

Abstract

Currently, the genetic programming version of the gene-pool optimal mixing evolutionary algorithm (GP-GOMEA) is among the top-performing algorithms for symbolic regression (SR). A key strength of GP-GOMEA is its way of performing variation, which dynamically adapts to the emergence of patterns in the population. However, GP-GOMEA lacks a mechanism to optimize coefficients. In this paper, we study how fairly simple approaches for optimizing coefficients can be integrated into GP-GOMEA. In particular, we considered two variants of Gaussian coefficient mutation. We performed experiments using different settings on 23 benchmark problems, and used machine learning to estimate what aspects of coefficient mutation matter most. We find that the most important aspect is that the number of coefficient mutation attempts needs to be commensurate with the number of mixing operations that GP-GOMEA performs. We applied GP-GOMEA with the best-performing coefficient mutation approach to the data sets of SRBench, a large SR benchmark, for which a ground-truth underlying equation is known. We find that coefficient mutation can help re-discovering the underlying equation by a substantial amount, but only when no noise is added to the target variable. In the presence of noise, GP-GOMEA with coefficient mutation discovers alternative but similarly-accurate equations.