A global representation scheme for genetic algorithms

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.