Genetic programming, the reflection of chaos, and the bootstrap: towards a useful test for chaos

  • Authors:
  • E. Howard N. Oakley

  • Affiliations:
  • EHN & DIJ Oakley, Wroxall, Ventnor, UK

  • Venue:
  • GECCO '96 Proceedings of the 1st annual conference on Genetic and evolutionary computation
  • Year:
  • 1996

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Abstract

This study assessed the use of genetic programming (GP) to diagnose chaos. Fifty GP runs were performed on chaotic data, generated from the Mackey-Glass delay differential equation, on one surrogate with the same Fourier power spectrum and statistics but without chaotic dynamics, and on a random walk series. Single runs were performed on 50 different surrogates of the chaotic series. Fitness was measured across 5 separate forecast periods of 65 points each, each based upon 10 prior input data points. Fittest program fragments for the chaotic series evolved later and were more complicated than those for the surrogates. Relative to fitnesses achieved by constant linear predictions, fitnesses from the chaotic series were also better. Random walk data resulted in an impoverished GP process, with quick evolution of simple program fragments but no later evolutionary improvement. This comparative test merits assessment on other datasets, and its implications with respect to the statistical bootstrap and GP estimation are discussed.