Correlation analysis of coupled fitness landscapes

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.

[1]  Stewart W. Wilson.  GA-Easy Does Not Imply Steepest-Ascent Optimizable , 1991, ICGA.

[2]  S. Kauffman,et al.  Towards a general theory of adaptive walks on rugged landscapes. , 1987, Journal of theoretical biology.

[3]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[4]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[5]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[6]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[7]  James P. Crutchfield,et al.  Resource sharing and coevolution in evolving cellular automata , 1999, IEEE Trans. Evol. Comput..

[8]  Peter F. Stadler,et al.  Amplitude Spectra of Fitness Landscapes , 1998, Adv. Complex Syst..

[9]  E. Ziegel.  Introduction to the Theory and Practice of Econometrics , 1989 .

[10]  P. Stadler.  Landscapes and their correlation functions , 1996 .

[11]  Marc Lipsitch,et al.  Adaptation on Rugged Landscapes Generated by Iterated Local Interactions of Neighboring Genes , 1991, ICGA.

[12]  C. Granger,et al.  Forecasting Economic Time Series. , 1988 .

[13]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[14]  Melanie Mitchell,et al.  Relative Building-Block Fitness and the Building Block Hypothesis , 1992, FOGA.

[15]  Wim Hordijk,et al.  A Measure of Landscapes , 1996, Evolutionary Computation.

[16]  W. Daniel Hillis,et al.  Co-evolving parasites improve simulated evolution as an optimization procedure , 1990 .

[17]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[18]  Daniel A. Levinthal.  Adaptation on rugged landscapes , 1997 .

[19]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[20]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[21]  W. Hordijk.  Correlation analysis of the synchronizing-CA landscape , 1997 .

[22]  B. Drossel.  Biological evolution and statistical physics , 2001, cond-mat/0101409.

[23]  Bernard Manderick,et al.  The Genetic Algorithm and the Structure of the Fitness Landscape , 1991, ICGA.

[24]  L. Altenberg.  B2.7.2 NK Fitness Landscapes , 1997 .

[25]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

[26]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[27]  Gerhard Hummer,et al.  Multi-basin dynamics of a protein in a crystal environment , 1997 .

[28]  Hugues Juillé,et al.  Coevolutionary Learning and the Design of Complex Systems , 1999, Adv. Complex Syst..

[29]  E. Weinberger,et al.  Correlated and uncorrelated fitness landscapes and how to tell the difference , 1990, Biological Cybernetics.

[30]  S. Kauffman,et al.  Coevolution to the edge of chaos: coupled fitness landscapes, poised states, and coevolutionary avalanches. , 1991, Journal of theoretical biology.

[31]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[32]  Peter F. Stadler,et al.  Canonical approximation of fitness landscapes , 1996 .

[33]  Terry Jones,et al.  One Operator, One Landscape , 1995 .

[34]  Peter F. Stadler,et al.  Towards a theory of landscapes , 1995 .

[35]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[36]  Melanie Mitchell,et al.  The royal road for genetic algorithms: Fitness landscapes and GA performance , 1991 .