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Correlation Analysis of Coupled Fitness Landscapes

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Recent Advances in the Theory and Application of Fitness Landscapes

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 6))

Abstract

In this chapter we present an overview of a statistical analysis to measure and express the correlation structure of fitness landscapes. This correlation analysis is then applied to both static and coupled fitness landscapes as generated by the NK-model and the NKC-model, respectively. An overview of the main results is provided, which shows that this correlation analysis can indeed be applied in a meaningful way to coupled fitness landscapes. This can provide a direct and useful link to the actual search performance of evolutionary algorithms that use a coevolutionary approach.

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References

  1. Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press (1996)

    Google Scholar 

  2. Box, G.E.P., Jenkins, G.M.: Time Series Analysis, Forecasting and Control. Holden Day (1970)

    Google Scholar 

  3. Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer (2003)

    Google Scholar 

  4. Forrest, S., Mitchell, M.: Relative building-block fitness and the building-block hypothesis. In: Whitley, D. (ed.) Foundations of Genetic Algorithms 2, pp. 109–126. Morgan Kaufmann (1993)

    Google Scholar 

  5. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley (1989)

    Google Scholar 

  6. Granger, C.W.J., Newbold, P.: Forecasting Economic Time Series, 2nd edn. Academic Press (1986)

    Google Scholar 

  7. Hillis, W.D.: Co-evolving parasites improve simulated evolution as an optimization procedure. Physica D 42, 228–234 (1990)

    Article  Google Scholar 

  8. Holland, J.H.: Adaptation in Natural and Artificial Systems, 2nd edn. MIT Press (1992)

    Google Scholar 

  9. Hordijk, W.: A measure of landscapes. Evolutionary Computation 4, 335–360 (1996)

    Article  Google Scholar 

  10. Hordijk, W.: Correlation analysis of the synchronizing-CA landscape. Physica D 107, 255–264 (1997)

    Article  Google Scholar 

  11. Hordijk, W., Kauffman, S.A.: Correlation analysis of coupled fitness landscapes. Complexity 10(6), 41–49 (2005)

    Article  MathSciNet  Google Scholar 

  12. Hordijk, W., Stadler, P.F.: Amplitute spectra of fitness landscapes. Advances in Complex Systems 1(1), 39–66 (1998)

    Article  MATH  Google Scholar 

  13. Jones, T.: Evolutionary Algorithms, Fitness Landscapes, and Search. PhD thesis, University of New Mexico, Albuquerque, NM, USA (1995)

    Google Scholar 

  14. Jones, T.: One operator, one landscape. SFI working paper 95-02-025 (1995)

    Google Scholar 

  15. Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Eshelman, L.J. (ed.) Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann (1995)

    Google Scholar 

  16. Judge, G.G., Hill, R.C., Griffiths, W.E., Lutkepohl, H., Lee, T.C.: Introduction to the Theory and Practice of Econometrics, 2nd edn. John Wiley & Sons (1988)

    Google Scholar 

  17. Juillé, H., Pollack, J.B.: Coevolutionary learning and the design of complex systems. Advances in Complex Systems 2(4), 371–394 (2000)

    Article  Google Scholar 

  18. Kauffman, S.A.: Adaptation on rugged fitness landscapes. In: Stein, D. (ed.) Lectures in the Sciences of Complexity, pp. 527–618. Addison-Wesley (1989)

    Google Scholar 

  19. Kauffman, S.A.: The Origins of Order. Oxford University Press (1993)

    Google Scholar 

  20. Kauffman, S.A., Johnson, S.: Coevolution to the edge of chaos: Coupled fitness landscapes, poised states, and coevolutionary avalanches. Journal of Theoretical Biology 149, 467–505 (1991)

    Article  Google Scholar 

  21. Kauffman, S.A., Levin, S.: Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology 128, 11–45 (1987)

    Article  MathSciNet  Google Scholar 

  22. Lipsitch, M.: Adaptation on rugged landscapes generated by iterated local interactions of neighboring genes. In: Belew, R.K., Booker, L.B. (eds.) Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 128–135. Morgan Kaufmann (1991)

    Google Scholar 

  23. Manderick, B., de Weger, M., Spiessens, P.: The genetic algorithm and the structure of the fitness landscape. In: Belew, R.K., Booker, L.B. (eds.) Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 143–150. Morgan Kaufmann (1991)

    Google Scholar 

  24. Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press (1996)

    Google Scholar 

  25. Mitchell, M., Forrest, S., Holland, J.H.: The royal road for genetic algorithms: Fitness landscapes and GA performance. In: Varela, F.J., Bourgine, P. (eds.) Toward a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life, pp. 245–254. MIT Press (1992)

    Google Scholar 

  26. Stadler, P.F.: Towards a theory of landscapes. In: Lopéz-Peña, R., Capovilla, R., García-Pelayo, R., Waelbroeck, H., Zertuche, F. (eds.) Complex Systems and Binary Networks, pp. 77–163. Springer (1995)

    Google Scholar 

  27. Stadler, P.F.: Fitness landscapes. In: Lässig, M., Valleriani, A. (eds.) Biological Evolution and Statistical Physics. Lecture Notes in Physics, pp. 183–204. Springer (2002)

    Google Scholar 

  28. Weinberger, E.D.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics 63, 325–336 (1990)

    Article  MATH  Google Scholar 

  29. Werfel, J., Mitchell, M., Crutchfield, J.P.: Resource sharing and coevolution in evolving cellular automata. IEEE Transactions on Evolutionary Computation 4(4), 388–393 (2000)

    Article  Google Scholar 

  30. Wilson, S.W.: GA-easy does not imply steepest-ascent optimizable. In: Belew, R.K., Booker, L.B. (eds.) Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 85–89. Morgan Kaufmann (1991)

    Google Scholar 

  31. Wright, S.: The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Jones, D.F. (ed.) Proceedings of the Sixth International Congress on Genetics, vol. 1, pp. 356–366 (1932)

    Google Scholar 

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Author information

Authors and Affiliations

  1. SmartAnalytiX.com, Lausanne, Switzerland

    Wim Hordijk

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  1. Wim Hordijk
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Correspondence to Wim Hordijk .

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Editors and Affiliations

  1. Faculty of Electrical Engineering & Information Technology, HTWK Leipzig University of Applied Sciences, Leipzig, Germany

    Hendrik Richter

  2. Department of Computer Science, University of Pretoria, Pretoria, South Africa

    Andries Engelbrecht

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Hordijk, W. (2014). Correlation Analysis of Coupled Fitness Landscapes. In: Richter, H., Engelbrecht, A. (eds) Recent Advances in the Theory and Application of Fitness Landscapes. Emergence, Complexity and Computation, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41888-4_13

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  • DOI: https://doi.org/10.1007/978-3-642-41888-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41887-7

  • Online ISBN: 978-3-642-41888-4

  • eBook Packages: EngineeringEngineering (R0)

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