research-article

Free access

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

Author:

E. Howard N. OakleyAuthors Info & Claims

Proceedings of the 1st annual conference on genetic programming

Pages 175 - 181

Published: 28 July 1996 Publication History

PDF eReader

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.

References

[1]

{Casdagli et al., 1992} M. Casdagli, D. des Jardins, S. Eubank, J. D. Farmer, J. Gibson, and J. Theiler. 1992. Nonlinear modeling of chaotic time series: theory and applications. In J. H. Kim and J. Stringer (editors). Applied Chaos. New York, NY: Wiley-Interscience. Pages 335--380.

Google Scholar

[2]

{Efron and Tibshirani, 1993} B. Efron and R. J. Tibshirani. 1993. An Introduction to the Bootstrap, Monographs on Statistics and Applied Probability. Volume 57. New York, NY: Chapman and Hall.

Google Scholar

[3]

{Gershenfeld and Weigend, 1994} N. A. Gershenfeld and A. S. Weigend. 1994. The future of time series: learning and understanding. In A. S. Weigend and N. A. Gershenfeld (editors). Time Series Prediction: Forecasting the future and understanding the past. Reading, MA: Addison-Wesley. Pages 1--70.

Google Scholar

[4]

{Glass and Kaplan, 1994} L. Glass and D. Kaplan. 1994. Complex dynamics in physiology and medicine. In A. S. Weigend and N. A. Gershenfeld (editors). Time Series Prediction: Forecasting the future and understanding the past. Reading, MA: Addison-Wesley. Pages 513--528.

Google Scholar

[5]

{Koza, 1992} J. R. Koza. 1992. Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge, MA: The MIT Press.

Digital Library

Google Scholar

[6]

{Koza, 1994} J. R. Koza. 1992. Genetic Programming II: Automatic Discovery of Reusable Programs. Cambridge, MA: The MIT Press.

Digital Library

Google Scholar

[7]

{Mackey and Glass, 1977} M. C. Mackey and L. Glass. 1977. Oscillation and chaos in physiological control systems. Science. Volume 197. Pages 287--289.

Google Scholar

[8]

{Oakley, 1994a} E. H. N. Oakley. 1994. The application of genetic programming to the investigation of short, noisy, chaotic data series. In T. C. Fogarty (editor). Evolutionary Programming, Lecture Notes in Computer Science. Number 865. Berlin, Germany: Springer-Verlag. Pages 320--332.

Digital Library

Google Scholar

[9]

{Oakley, 1994b} E. H. N. Oakley. 1994. Two scientific applications of genetic programming: stack filters and non-linear equation fitting to chaotic data. In K. E. Kinnear Jr. (editor). Advances in Genetic Programming. Cambridge, MA: The MIT Press. Pages 369--389.

Digital Library

Google Scholar

[10]

{Oakley, 1995} E. H. N. Oakley. 1995. Genetic programming as a means of assessing and reflecting chaos. In Genetic Programming, AAAI-95 Fall Symposium Series. American Association for Artificial Intelligence. November 1995. Pages 68--72.

Google Scholar

[11]

{Ruelle, 1990} D. Ruelle. 1990. Deterministic chaos: the science and the fiction. Proceedings of the Royal Society of London A. Volume 427. Pages 241--248.

Google Scholar

[12]

{Theiler et al., 1992} J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, and J. D. Farmer. 1992. Using surrogate data to detect nonlinearity in time series. In M. Casdagli and S. Eubank (editors). Nonlinear Modeling and Forecasting. Redwood City, CA: Addison-Wesley. Pages 163--188.

Google Scholar

Cited By

View all

Fitzgerald JAzad RRyan CAlba E(2013)A bootstrapping approach to reduce over-fitting in genetic programmingProceedings of the 15th annual conference companion on Genetic and evolutionary computation10.1145/2464576.2482690(1113-1120)Online publication date: 6-Jul-2013
https://dl.acm.org/doi/10.1145/2464576.2482690
Kaboudan M(2000)Genetic Programming Prediction of Stock PricesComputational Economics10.1023/A:100876840404616:3(207-236)Online publication date: 1-Dec-2000
https://dl.acm.org/doi/10.1023/A%3A1008768404046

Recommendations

A rapid chaos genetic algorithm
ICSI'10: Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part I

Genetic algorithm is an evolutionary algorithm It is particularly suitable for solving NP-complete optimization problems In this paper, we propose a rapid genetic algorithm based on chaos mechanism We introduce the chaos mechanism into the genetic ...
An Improved Mutative Scale Chaos Optimization Quantum Genetic Algorithm
ICNC '08: Proceedings of the 2008 Fourth International Conference on Natural Computation - Volume 06

The theory of chaos optimization is introduced in this paper; and through improving the constringency strategy of mutative scale chaos optimization method, we can enhance the efficiency and the performance of chaos optimization method; then aiming at ...
Genetic Algorithm using Theory of Chaos

This paper is focused on genetic algorithm with chaotic crossover operator. We have performed some experiments to study possible use of chaos in simulated evolution. A novel genetic algorithm with chaotic optimization operation is proposed to ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

Proceedings of the 1st annual conference on genetic programming

July 1996

571 pages

ISBN:0262611279

General Chair:
John R. Koza
Stanford University

Publisher

MIT Press

Cambridge, MA, United States

Publication History

Published: 28 July 1996

Qualifiers

Research-article

Acceptance Rates

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
113
Total Downloads

Downloads (Last 12 months)27
Downloads (Last 6 weeks)3

Reflects downloads up to 16 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Fitzgerald JAzad RRyan CAlba E(2013)A bootstrapping approach to reduce over-fitting in genetic programmingProceedings of the 15th annual conference companion on Genetic and evolutionary computation10.1145/2464576.2482690(1113-1120)Online publication date: 6-Jul-2013
https://dl.acm.org/doi/10.1145/2464576.2482690
Kaboudan M(2000)Genetic Programming Prediction of Stock PricesComputational Economics10.1023/A:100876840404616:3(207-236)Online publication date: 1-Dec-2000
https://dl.acm.org/doi/10.1023/A%3A1008768404046

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Recommendations

A rapid chaos genetic algorithm

An Improved Mutative Scale Chaos Optimization Quantum Genetic Algorithm

Genetic Algorithm using Theory of Chaos

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Acceptance Rates

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

PDF

eReader

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations