Comparatively to Genetic Programming, the implementation of
Automatically Defined Functions in Gene Expression Programming is
very simple because it stands on the shoulders of the multigenic
system with static linking and, therefore, requires just a small
addition to make it work. And because the cellular system of GEP
with ADFs, like all GEP systems, continues to be totally encoded in
a simple linear genome, it poses no constraints whatsoever to the
action of the genetic operators and, therefore, these systems can
also evolve efficiently (indeed, all the genetic operators of GEP
were easily extended to the homeotic genes). As a comparison, the
implementation of ADFs in GP adds additional constraints to the
already constrained genetic operators in order to ensure the
integrity of the different structural branches of the parse tree.
Furthermore, due to its mammothness, the implementation of multiple
main programs in Genetic Programming is prohibitive, whereas in Gene
Expression Programming the creation of a multicellular system
encoding multiple main programs is a child's play.
Indeed, another advantage of the cellular system of GEP, is that it
can easily grow into a multicellular one, encoding not just one but
multiple cells or main programs, each using a different set of ADFs.
These multicellular systems have multiple applications, some of
which were already illustrated in this work, but their real
potential resides in solving problems with multiple outputs where
each cell encodes a program involved in the identification of a
certain class or pattern. Indeed, the high performance exhibited by
the multicellular system in this work gives hope that this system
can be fruitfully explored to solve much more complex problems. In
fact, in this work, not only the multicellular but also the
unicellular and the multigenic system with static linking, were all
far from stretched to their limits as the small population sizes of
just 50 individuals used in all the experiments of this work
indicate. As a comparison, to solve this same problem, the GP system
with ADFs uses already populations of 4,000 individuals.
And yet another advantage of the ADFs of Gene Expression
Programming, is that they are free to become functions of one or
several arguments, being this totally decided by evolution itself.
Again, in GP, the number of arguments each ADF takes must be a
priori decided and cannot be changed during the course of evolution
lest invalid structures are created.
And finally, the cellular system (and multicellular also) encoding
ADFs with random numerical constants was for the first time
described in this work. Although their performance was also compared
to other systems, the main goal was to show that ADFs with random
numerical constants can also evolve efficiently, extending not only
their appeal but also the range of their potential applications.