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

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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.
OriginalspracheEnglisch
TitelProceedings - 2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2022
Redakteure/-innenBruno Buchberger, Mircea Marin, Viorel Negru, Daniela Zaharie
Herausgeber (Verlag)IEEE
Seiten304-310
Seitenumfang7
ISBN (elektronisch)978-1-6654-6545-8
ISBN (Print)978-1-6654-6546-5
DOIs
PublikationsstatusVeröffentlicht - 2023

Publikationsreihe

NameProceedings - 2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2022

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