@inproceedings{955d78af42d94a02bbc76fd4730d05b1,
title = "Local Optimization Often is Ill-conditioned in Genetic Programming for Symbolic Regression.",
abstract = "Gradient-based local optimization 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 optimization. The effectiveness of NLS algorithms depends on appropriate scaling and conditioning of the optimization 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 = "Evolutionary computing and genetic algorithms, Gradient methods, Least squares methods, Nonlinear approximation",
author = "Gabriel Kronberger",
note = "Funding Information: G.K. acknowledges support by the Christian Doppler Re- search Association and the Austrian Federal Ministry of Dig- ital and Economic Affairs within the Josef Ressel Center for Symbolic Regression. The author thanks the maintainers of the GP bibliography for providing such a well-curated BibTeX database. Funding Information: G.K. acknowledges support by the Christian Doppler Research Association and the Austrian Federal Ministry of Digital and Economic Affairs within the Josef Ressel Center for Symbolic Regression. The author thanks the maintainers of the GP bibliography for providing such a well-curated BibTeX database. Publisher Copyright: {\textcopyright} 2022 IEEE.",
year = "2023",
doi = "10.1109/SYNASC57785.2022.00055",
language = "English",
isbn = "978-1-6654-6546-5",
series = "Proceedings - 2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2022",
publisher = "IEEE",
pages = "304--310",
editor = "Bruno Buchberger and Mircea Marin and Viorel Negru and Daniela Zaharie",
booktitle = "Proceedings - 2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2022",
}