Nonlinear Least Squares Optimization of Constants in Symbolic Regression

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@InProceedings{3737,
  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",
}

Genetic Programming entries for Michael Kommenda Michael Affenzeller Gabriel Kronberger Stephan M Winkler

Citations