Local Optimization Often is Ill-conditioned in Genetic Programming for Symbolic Regression

Created by W.Langdon from gp-bibliography.bib Revision:1.7656

@InProceedings{Kronberger:2022:SYNASC,

• author = "Gabriel Kronberger",
• booktitle = "2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)",
• title = "Local Optimization Often is Ill-conditioned in Genetic Programming for Symbolic Regression",
• year = "2022",
• pages = "304--310",
• abstract = "Gradient-based local optimisation has been shown to improve results of genetic programming (GP) for symbolic regression. Several state-of-the-art GP implementations use iterative nonlinear least squares (NLS) algorithms such as the Levenberg-Marquardt algorithm for local optimisation. The effectiveness of NLS algorithms depends on appropriate scaling and conditioning of the optimisation problem. This has so far been ignored in symbolic regression and GP literature. In this study we use a singular value decomposition of NLS Jacobian matrices to determine the numeric rank and the condition number. We perform experiments with a GP implementation and six different benchmark datasets. Our results show that rank-deficient and ill-conditioned Jacobian matrices occur frequently and for all datasets. The issue is less extreme when restricting GP tree size and when using many non-linear functions in the function set.",
• keywords = "genetic algorithms, genetic programming, Jacobian matrices, Scientific computing, Benchmark testing, Approximation algorithms, Iterative algorithms, Optimisation, Evolutionary computing and Nonlinear approximation, Least squares methods, Gradient methods",
• DOI = "doi:10.1109/SYNASC57785.2022.00055",
• ISSN = "2470-881X",
• month = sep,
• notes = "Also known as \cite{10130940}",

}

Genetic Programming entries for Gabriel Kronberger

Citations