Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2001-05-10
Nonlinear Sciences
Adaptation and Self-Organizing Systems
9 pages latex, 1 style file proceedings.sty. To be published in Proceedings of GECCO 2001, Morgan Kauffman (2001) (submitted J
Scientific paper
We extend a recently developed exact schema based, or coarse grained, formulation of genetic dynamics \cite{stewael,stewael1,stewael2} and its associated exact Schema theorem to an arbitrary selection scheme and a general crossover operator. We show that the intuitive``building block'' interpretation of the former is preserved leading to hierarchical formal solutions of the equations that upon iteration lead to new results for the limiting distribution of a population in the case of 1-point crossover and ``weak'' selection, where we define quantitatively ``weak''. We also derive an exact, analytic form for the population distribution as a function of time for a flat landscape and 1-point crossover.
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