Nonlinear least squares optimization of constants in symbolic regression

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4 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationComputer Aided Systems Theory, EUROCAST 2013 - 14th International Conference, Revised Selected Papers
Number of pages8
EditionPART 1
ISBN (Print)9783642538551
Publication statusPublished - 2013
Event14th International Conference on Computer Aided Systems Theory, Eurocast 2013 - Las Palmas de Gran Canaria, Spain
Duration: 10 Feb 201315 Feb 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8111 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Conference on Computer Aided Systems Theory, Eurocast 2013
CityLas Palmas de Gran Canaria


  • Automatic Differentiation
  • Constant Optimization
  • Genetic Programming
  • Levenberg-Marquard Algorithm
  • Symbolic Regression


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