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C. FERREIRA In N. Nedjah, L. de M. Mourelle, A. Abraham, eds., Genetic Systems Programming: Theory and Experiences, Studies in Computational Intelligence, Vol. 13, pp. 21-56, Springer-Verlag, 2006.

Automatically Defined Functions in Gene Expression Programming

Homeotic Genes and the Cellular System of GEP
Homeotic genes have exactly the same kind of structure as conventional genes and are built using an identical process. They also contain a head and a tail domain, with the heads containing, in this case, linking functions (so called because they are actually used to link different ADFs) and a special class of terminals genic terminals representing conventional genes, which, in the cellular system, encode different ADFs; the tails contain obviously only genic terminals.

Consider, for instance, the following chromosome:




It codes for three conventional genes and one homeotic gene (shown in blue). The conventional genes encode, as usual, three different sub-ETs, with the difference that now these sub-ETs will act as ADFs and, therefore, may be invoked multiple times from different places. And the homeotic gene controls the interactions between the different ADFs (Figure 8). As you can see in Figure 8, in this particular case, ADF0 is used twice in the main program, whereas ADF1 and ADF2 are both used just once.

Figure 8. Expression of a unicellular system with three Automatically Defined Functions. a) The chromosome composed of three conventional genes and one homeotic gene (shown in bold). b) The ADFs codified by each conventional gene. c) The main program or cell.

It is worth pointing out that homeotic genes have their specific length and their specific set of functions. And these functions can take any number of arguments (functions with 1, 2, 3, , n, arguments). For instance, in the particular case of chromosome (11), the head length of the homeotic gene hH is equal to five, whereas for the conventional genes h = 4; the function set used in the homeotic gene FH consists of FH = {+, -, *, /, Q}, whereas for the conventional genes the function set consists of F = {+, -, *, /}. As shown in Figure 8, this cellular system is not only a form of elegantly allowing the evolution of linking functions in multigenic systems but also an extremely elegant way of encoding ADFs that can be called an arbitrary number of times from an arbitrary number of different places.


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