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
Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press (1996)
Box, G.E.P., Jenkins, G.M.: Time Series Analysis, Forecasting and Control. Holden Day (1970)
Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer (2003)
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)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley (1989)
Granger, C.W.J., Newbold, P.: Forecasting Economic Time Series, 2nd edn. Academic Press (1986)
Hillis, W.D.: Co-evolving parasites improve simulated evolution as an optimization procedure. Physica D 42, 228–234 (1990)
Holland, J.H.: Adaptation in Natural and Artificial Systems, 2nd edn. MIT Press (1992)
Hordijk, W.: A measure of landscapes. Evolutionary Computation 4, 335–360 (1996)
Hordijk, W.: Correlation analysis of the synchronizing-CA landscape. Physica D 107, 255–264 (1997)
Hordijk, W., Kauffman, S.A.: Correlation analysis of coupled fitness landscapes. Complexity 10(6), 41–49 (2005)
Hordijk, W., Stadler, P.F.: Amplitute spectra of fitness landscapes. Advances in Complex Systems 1(1), 39–66 (1998)
Jones, T.: Evolutionary Algorithms, Fitness Landscapes, and Search. PhD thesis, University of New Mexico, Albuquerque, NM, USA (1995)
Jones, T.: One operator, one landscape. SFI working paper 95-02-025 (1995)
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)
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)
Juillé, H., Pollack, J.B.: Coevolutionary learning and the design of complex systems. Advances in Complex Systems 2(4), 371–394 (2000)
Kauffman, S.A.: Adaptation on rugged fitness landscapes. In: Stein, D. (ed.) Lectures in the Sciences of Complexity, pp. 527–618. Addison-Wesley (1989)
Kauffman, S.A.: The Origins of Order. Oxford University Press (1993)
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)
Kauffman, S.A., Levin, S.: Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology 128, 11–45 (1987)
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)
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)
Mitchell, M.: An Introduction to Genetic Algorithms. MIT Press (1996)
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)
Stadler, P.F.: Towards a theory of landscapes. In: Lopéz-Peña, R., Capovilla, R., GarcÃa-Pelayo, R., Waelbroeck, H., Zertuche, F. (eds.) Complex Systems and Binary Networks, pp. 77–163. Springer (1995)
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)
Weinberger, E.D.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics 63, 325–336 (1990)
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)
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)
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)
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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
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