Effects of constant optimization by nonlinear least squares minimization in symbolic regression

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42 Citations (Scopus)

Abstract

In this publication a constant optimization approach for symbolic regression is introduced to separate the task of finding the correct model structure from the necessity to evolve the correct numerical constants. A gradient-based nonlinear least squares optimization algorithm, the Levenberg- Marquardt (LM) algorithm, is used for adjusting constant values in symbolic expression trees during their evolution. The LM algorithm depends on gradient information consisting of partial derivations of the trees, which are obtained by automatic differentiation. The presented constant optimization approach is tested on several benchmark problems and compared to a standard genetic programming algorithm to show its effectiveness. Although the constant optimization involves an overhead regarding the execution time, the achieved accuracy increases significantly as well as the ability of genetic programming to learn from provided data. As an example, the Pagie-1 problem could be solved in 37 out of 50 test runs, whereas without constant optimization it was solved in only 10 runs. Furthermore, different configurations of the constant optimization approach (number of iterations, probability of applying constant optimization) are evaluated and their impact is detailed in the results section.

Original languageEnglish
Title of host publicationGECCO 2013 - Proceedings of the 2013 Genetic and Evolutionary Computation Conference Companion
PublisherACM Sigevo
Pages1121-1128
Number of pages8
ISBN (Print)9781450319645
DOIs
Publication statusPublished - 2013
Event15th Annual Conference on Genetic and Evolutionary Computation, GECCO 2013 - Amsterdam, Netherlands
Duration: 6 Jul 201310 Jul 2013

Publication series

NameGECCO 2013 - Proceedings of the 2013 Genetic and Evolutionary Computation Conference Companion

Conference

Conference15th Annual Conference on Genetic and Evolutionary Computation, GECCO 2013
CountryNetherlands
CityAmsterdam
Period06.07.201310.07.2013

Keywords

  • Automatic differentation
  • Constant optimization
  • Nonlinear least squares optimization
  • Symbolic regression

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