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Similarity-Based Analysis of Population Dynamics in Genetic Programming Performing Symbolic Regression

  • Stephan M. WinklerEmail author
  • Michael Affenzeller
  • Bogdan Burlacu
  • Gabriel Kronberger
  • Michael Kommenda
  • Philipp Fleck
Chapter
Part of the Genetic and Evolutionary Computation book series (GEVO)

Abstract

Population diversity plays an important role in the evolutionary dynamics of genetic programming (GP). In this paper we use structural and semantic similarity measures to investigate the evolution of diversity in three GP algorithmic flavors: standard GP, offspring selection GP (OS-GP), and age-layered population structure GP (ALPS-GP). Empirical measurements on two symbolic regression benchmark problems reveal important differences between the dynamics of the tested configurations. In standard GP, after an initial decrease, population diversity remains almost constant until the end of the run. The higher variance of the phenotypic similarity values suggests that small changes on individual genotypes have significant effects on their corresponding phenotypes. By contrast, strict offspring selection within the OS-GP algorithm causes a significantly more pronounced diversity loss at both genotypic and, in particular, phenotypic levels. The pressure for adaptive change increases phenotypic robustness in the face of genotypic perturbations, leading to less genotypic variability on the one hand, and very low phenotypic diversity on the other hand. Finally, the evolution of similarities in ALPS-GP follows a periodic pattern marked by the time interval when the bottom layer is reinitialized with new individuals. This pattern is easily noticed in the lower layers characterized by shorter migration intervals, and becomes less and less noticeable on the upper layers.

Keywords

Genetic programming Symbolic regression Population dynamics Genetic diversity Phenotypic diversity Offspring selection Age-layered population structure ALPS 

Notes

Acknowledgements

The work described in this paper was done within the COMET Project Heuristic Optimization in Production and Logistics (HOPL), #843532 funded by the Austrian Research Promotion Agency (FFG).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Stephan M. Winkler
    • 1
    • 2
    Email author
  • Michael Affenzeller
    • 1
    • 2
  • Bogdan Burlacu
    • 1
    • 2
  • Gabriel Kronberger
    • 1
  • Michael Kommenda
    • 1
    • 2
  • Philipp Fleck
    • 1
  1. 1.Heuristic and Evolutionary Algorithms LaboratoryUniversity of Applied Sciences Upper AustriaHagenbergAustria
  2. 2.Institute for Formal Models and VerificationJohannes Kepler UniversityLinzAustria

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