Abstract
Modelling the behaviour of genetic algorithms has concentrated on Markov chain analysis. However, Markov chains yield little insight into the dynamics of the underlying mechanics and processes. Thus, a framework and methodology for global modelling and visualisation of genetic algorithms is described, using tools from the field of Information Theory. Using Principal Component Analysis (PCA) based on the Karhunen-Loève transform, a generation (instance of a population) is transformed into a compact low dimensional eigenspace representation. A pattern vector (set of weights) is calculated for each population of strings, by projecting it into the eigenspace. A 3D manifold or global signature is derived from the set of computed pattern vectors.
Principal Components Analysis is applied to a GA parameterised by three encoding schemes — binary, E-code and Gray — and a test platform consisting of twelve functions. The resultant manifolds are described and correlated. The paper is concluded with a discussion of possible interpretations of the derived results, and potential extensions to the proposed methodology.
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Collins, J.J., Eaton, M. (1997). A global representation scheme for genetic algorithms. In: Reusch, B. (eds) Computational Intelligence Theory and Applications. Fuzzy Days 1997. Lecture Notes in Computer Science, vol 1226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62868-1_92
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DOI: https://doi.org/10.1007/3-540-62868-1_92
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