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Abstract:
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In this tutorial we will look at the mathematical description of the underlying dynamics of some simple genetic algorithms. Beginning with selection-mutation GAs, we will study the effects that fixed-points of the evolution equations have on population dynamics, introducing the concepts of "metastability" and "neutral networks". The class of quadratic maps (in particular, crossover) will be defined. Standard crossover operators have a rich algebraic structure which can be studied using elementary group theory, enabling us to relate properties of the operators with structural aspects of the search landscape. We will look at some theorems and conjectures concerning selection-crossover GAs. Other examples of quadratic maps include tournament selection and co-evolutionary selection (in which fitness depends on the state of the current population).
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