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According to this definition of functionality, an enzyme's shape is derived
from both its own activity and the shape of its specificities. The shapes of an
enzyme's active specificities, moreover, are also the shapes of the enzymes
that this enzyme would prefer to bind during development, its ideal substrates.
Consequently, this enzyme's functionality also captures in part the function-
alities of its ideal substrates, which also capture in part the functionalities of
their ideal substrates. Following this logic recursively, it becomes evident that
an enzyme's functionality captures, in part, the functionality of its ideal sub-
trees. Since functionality is also derived from activity, the functionality of an
ideal subtree implicitly captures information regarding the occurrence of each
activity within the subtree.
However, functionality only captures a profile of the functions and terminals,
weighted by depth, within an enzyme's ideal subtrees. It does not capture the
hierarchical structure of the trees. Consequently, a functionality cannot describe
an enzyme uniquely. Nevertheless, functionality space is continuous, making it
unlikely that two nonidentical enzymes will both have the same functionality
and occur in the same program.
An enzyme's actual context depends on which other enzymes are present
within a program. This implies that it is both variant between programs and
indeterminate before development takes place. For both of these reasons, func-
tionality cannot, and does not, attempt to specify an enzyme's actual context. It
does, however, attempt to specify an enzyme's preferred context, which is the
most probable context, but like any specific context, is itself unlikely to occur
frequently.
Evolution
A program's genome, shown in Figure 3.8, is a linear array of enzymes grouped
into subarrays of glands, functional enzymes, and receptors. In enzyme GP, a
population of these genomes is evolved using a genetic algorithm with mutation
and crossover.
The genetic algorithm, depicted in Figure 3.9, uses a spatially distributed
population with a toroidal surface. The algorithm is generational, and during
each generation every member of the population is mated with a copy of its fittest
neighbor. The offspring are then subjected to mutation and fitness evaluation. If
the fitness of a child solution is equal to or higher than the fitness of the existing
solution at this location, then it replaces the existing solution. This is a locally
elitist policy that does not allow fit solutions to be lost, but at the same time
does not suffer the drawbacks of global elitism. For further details regarding
this GA, see Lones and Tyrrell [23].
Enzyme GP uses two forms of crossover. The first, a uniform crossover,
loosely models the mechanism of biological reproduction. The second, called
