Schemata Evolution and Building Blocks

Details Schemata Evolution and Building Blocks Schemata Evolution and Building Blocks

2000-06-30

arxiv.org/abs/nlin/0006048v1

Evolutionary Computation 7.2, 109 (1999)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

20 pages

Scientific paper

In the light of a recently derived evolution equation for genetic algorithms we consider the schema theorem and the building block hypothesis. We derive a schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The equation makes manifest the content of the building block hypothesis showing how fit schemata are constructed from fit sub-schemata. However, we show that generically there is no preference for short, low-order schemata. In the case where schema reconstruction is favored over schema destruction large schemata tend to be favored. As a corollary of the evolution equation we prove Geiringer's theorem.

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