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development of the individual. And the product of expression of such genes
consists of the main program or cell. Thus, homeotic genes determine which
genes are expressed in which cell and how the different sub-ETs (now work-
ing as ADFs) interact with one another. Or stated differently, homeotic genes
determine which ADFs are called upon in which main program and how
these ADFs are organized in each main program.
The importance of automatically defined functions and the advantages
they bring to automatic programming can only be understood if one analyzes
how they work and how the algorithm copes with their integration. Is evolu-
tion still smooth? Are there gains in performance? Is the system still simple
or excessively complicated? How does it compare to simpler systems with-
out ADFs? How does one go about integrating random numerical constants
in ADFs? Are these ADFs still manageable or excessively complex? Can the
multicellular system be explored to solve problems with multiple outputs?
Are there problems that can only be solved with ADFs? These are some of
the questions that we will try to address in this chapter by putting ADFs to
the test in problem solving. We will start by solving a simple modular func-
tion and analyzing a successful run in its entirety in order to understand how
such complex systems evolve. Then we will see how the cellular system
copes with a more challenging modular problem, the already familiar odd-
parity functions. And finally, we will put ADFs to the test by solving four
complex real-world problems with them: the first consists of Kepler's Third
Law; the second is the challenging analog circuit requiring numerical con-
stants that we studied in section 5.6.5; the third is again the breast cancer
classification problem so that we could compare the performance of the cel-
lular system with other simpler systems on a complex real-world problem;
and the last one is the interesting three-class prediction iris problem that will
be used to show how the multicellular system can be successfully used to
solve problems with multiple outputs.
6.1 Solving a Simple Modular Function with ADFs
In this section we are going to analyze a successful run in its entirety in order
to understand how populations of such complex entities composed of differ-
ent cells expressing different ADFs adapt, not only by changing the size and
shape of the basic building blocks (the ADFs) but also by creating/choosing
the main programs and changing their organization.
