Abstract
This is the first part of a two-part paper which
introduces a general schema theory for genetic
programming (GP) with subtree-swapping crossover. The
theory is based on a Cartesian node reference system
which makes it possible to describe programs as
functions over the space and allows one to model the
process of selection of the crossover points of
subtree-swapping crossovers as a probability
distribution over In Part I, we present these notions
and models and show how they can be used to calculate
useful quantities. In Part II we will show how this
machinery, when integrated with other definitions, such
as that of variable-arity hyperschema, can be used to
construct a general and exact schema theory for the
most commonly used types of GP.
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