The Entities of Gene Expression Programming - Gene Expression Programming - page 50

2.4 Other Levels of Complexity

As we have seen in the examples above, although a very simple system, gene
expression programming exhibits already a complex development and also
uses different chromosomal organizations. So far, we have been dealing with
genes (both conventional and homeotic) containing only head/tail domains.
But gene expression programming regularly uses other chromosomal organi-
zations that are more complex than the basic head/tail domain. These com-
plex chromosomal structures consist of clusters of functional units composed
of conventional head/tail domains plus one or more extra domains. The extra
domains usually code for several one-element sub-ETs. And all the sub-ETs
encoded in the different domains interact with one another, forming a more
complex entity with a complex network of interactions.
One such architecture was developed to manipulate random numerical
constants for function finding problems (Ferreira 2001, 2003). For instance,
the following chromosome contains an extra domain Dc (shown in bold)
encoding random numerical constants:

012345678901234 56789012
+*?+?*+a??aaa?? 09081345

(2.19)

As you can see in Figure 2.9, the translation of the head/tail domain is done
in the usual fashion, but, after translation, additional processing is needed in
order to replace the question marks in the tree by the numerical constants
they represent. In chapter 5, Numerical Constants and the GEP-RNC Algo-
rithm, we will learn how these sub-ETs interact with one another so that the
individual is fully expressed.
Multiple domains are also used to design neural networks totally encoded
in a linear genome. These neural networks are one of the most complex indi-
viduals evolved by GEP. In this case, the neural network architecture is en-
coded in a conventional head/tail domain, whereas the weights and thresh-
olds are encoded in two extra domains, Dw and Dt, each encoding several
one-element sub-ETs. For instance, the chromosome below contains two ex-
tra domains encoding the weights and the thresholds of the neural network
encoded in the head/tail domain (the domains are shown in different shades):
0123456789012345678 901234567890123456 789010
DUDTUDcdabdcabacbad 429984097914824092 675841 (2.20)
As you can see in Figure 2.10, the translation of the head/tail domain encod-
ing the neural network architecture is also done in the usual fashion, but the