An Empirical Study of Functional Complexity as an Indicator of Overfitting in Genetic Programming

  • Leonardo Trujillo
  • Sara Silva
  • Pierrick Legrand
  • Leonardo Vanneschi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6621)


Recently, it has been stated that the complexity of a solution is a good indicator of the amount of overfitting it incurs. However, measuring the complexity of a program, in Genetic Programming, is not a trivial task. In this paper, we study the functional complexity and how it relates with overfitting on symbolic regression problems. We consider two measures of complexity, Slope-based Functional Complexity, inspired by the concept of curvature, and Regularity-based Functional Complexity based on the concept of Hölderian regularity. In general, both complexity measures appear to be poor indicators of program overfitting. However, results suggest that Regularity-based Functional Complexity could provide a good indication of overfitting in extreme cases.


Genetic Programming Complexity Measure Functional Complexity Toxicity Problem Complexity Score 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Leonardo Trujillo
    • 1
  • Sara Silva
    • 2
    • 3
  • Pierrick Legrand
    • 4
    • 5
  • Leonardo Vanneschi
    • 2
    • 6
  1. 1.Instituto Tecnológico de TijuanaTijuanaMéxico
  2. 2.KDBIO groupINESC-ID LisboaLisbonPortugal
  3. 3.CISUC, ECOS groupUniversity of CoimbraPortugal
  4. 4.IMB, Institut de Mathématiques de Bordeaux, UMR CNRS 5251France
  5. 5.INRIA Bordeaux Sud-OuestFrance
  6. 6.Department of Informatics, Systems and Communication (D.I.S.Co.)University of Milano-BicoccaMilanItaly

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