Effects of reducing redundant parameters in parameter optimization for symbolic regression using genetic programming

Created by W.Langdon from gp-bibliography.bib Revision:1.8414

@Article{Kronberger:2025:jsc,

• author = "Gabriel Kronberger and Fabricio {Olivetti de Franca}",
• title = "Effects of reducing redundant parameters in parameter optimization for symbolic regression using genetic programming",
• journal = "Journal of Symbolic Computation",
• year = "2025",
• volume = "129",
• pages = "102413",
• keywords = "genetic algorithms, genetic programming, Symbolic regression, Machine learning, Expression rewriting, Equality saturation, Nonlinear least squares",
• ISSN = "0747-7171",
• URL = "https://www.sciencedirect.com/science/article/pii/S0747717124001172",
• DOI = "doi:10.1016/j.jsc.2024.102413",
• abstract = "Gradient-based local optimisation has been shown to improve results of genetic programming (GP) for symbolic regression (SR) - a machine learning method for symbolic equation learning. Correspondingly, several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms for local optimisation of parameters. An issue that has however mostly been ignored in SR and GP literature is overparameterization of SR expressions, and as a consequence, bad conditioning of NLS optimisation problem. The aim of this study is to analyse the effects of overparameterization on the NLS results and convergence speed, whereby we use Operon as an example GP/SR implementation. First, we demonstrate that numeric rank approximation can be used to detect overparameterization using a set of six selected benchmark problems. In the second part, we analyse whether the NLS results or convergence speed can be improved by simplifying expressions to remove redundant parameters with equality saturation. This analysis is done with the much larger Feynman symbolic regression benchmark set after collecting all expressions visited by GP, as the simplification procedure is not fast enough to use it within GP fitness evaluation. We observe that Operon frequently visits overparameterized solutions but the number of redundant parameters is small on average. We analysed the Pareto-optimal expressions of the first and last generation of GP, and found that for 70percent to 80percent of the simplified expressions, the success rate of reaching the optimum was better or equal than for the overparameterized form. The effect was smaller for the number of NLS iterations until convergence, where we found fewer or equal iterations for 51percent to 63percent of the expressions after simplification",

}

Genetic Programming entries for Gabriel Kronberger Fabricio Olivetti de Franca

Citations