- author = "Michael Kommenda and Michael Affenzeller and Gabriel K. Kronberger and Stephan M. Winkler",
- title = "Nonlinear Least Squares Optimization of Constants in Symbolic Regression",
- booktitle = "Computer Aided Systems Theory, EUROCAST 2013",
- year = "2013",
- editor = "Roberto Moreno-Diaz and Franz Pichler and Alexis Quesada-Arencibia",
- volume = "8111",
- series = "Lecture Notes in Computer Science",
- pages = "420--427",
- address = "Las Palmas de Gran Canaria, Spain",
- month = feb,
- publisher = "Springer",
- keywords = "genetic algorithms, genetic programming, Constant Optimization, Symbolic Regression, Levenberg-Marquard Algorithm, Automatic Differentiation",
- isbn13 = "978-3-642-53856-8",
-
URL = "
https://link.springer.com/chapter/10.1007/978-3-642-53856-8_53",
-
DOI = "
doi:10.1007/978-3-642-53856-8_53",
-
abstract = "In this publication a constant optimization approach
for symbolic regression by genetic programming is
presented. The Levenberg-Marquardt algorithm, a
nonlinear, least-squares method, tunes numerical values
of constants in symbolic expression trees to improve
their fit to observed data. The necessary gradient
information for the algorithm is obtained by automatic
programming, which efficiently calculates the partial
derivatives of symbolic expression trees.
The performance of the methodology is tested for standard and offspring selection genetic programming on four well-known benchmark datasets. Although constant optimization includes an overhead regarding the algorithm runtime, the achievable quality increases significantly compared to the standard algorithms. For example, the average coefficient of determination on the Poly-10 problem changes from 0.537 without constant optimization to over 0.8 with constant optimization enabled. In addition to the experimental results, the effect of different parameter settings like the number of individuals to be optimized is detailed.",
- notes = "Poly-10. Not SE",
