The Entities of Gene Expression Programming - Gene Expression Programming - page 36

only one node (when the first element of a gene is a terminal) and the largest
composed of as many nodes as the length of the gene (when all the elements
of the head are functions with maximum arity).
It is evident from the examples above, that any modification made in the
genome, no matter how profound, always results in a structurally correct
expression tree. Obviously, the structural organization of genes must be pre-
served, always maintaining the boundaries between head and tail and not
allowing symbols from the function set on the tail. We will pursue these
matters further in the next chapter (section 3.3) where the mechanisms and
the effects of different genetic operators are thoroughly analyzed.

2.1.3 Multigenic Chromosomes

In nature, chromosomes usually code for more than one gene, as complex
individuals require complex genomes. Indeed, the evolution of more com-
plex entities is only possible through the creation of multigenic genomes.
Not surprisingly, gene expression programming also explores the advantages
of multigenic systems.
The chromosomes of gene expression programming are usually composed
of more than one gene of equal length. For each problem, the number of
genes, as well as the length of the head, are chosen a priori. Each gene codes
for a sub-ET and the sub-ETs interact with one another forming a more com-
plex entity. The details of such interactions will be fully explained in section
2.2, Expression Trees and the Phenotype. For now we will focus exclusively
on the construction of sub-ETs from their respective genes.
Consider, for example, the following chromosome with length 39, com-
posed of three genes, each with h = 6 and a length of 13 (the tails are shown
in bold):

012345678901201234567890120123456789012
*Qb+*/ bbbabab -a+QbQ bbababa /ba-/* bbaaaaa

(2.9)

It has three open reading frames, and each ORF codes for a particular sub-
ET (Figure 2.2). We know already that the start of each ORF coincides with
the first element of the gene and, for the sake of clarity, for each gene it is
always indicated by position zero; the end of each ORF, though, is only evi-
dent upon construction of the respective sub-ET. As shown in Figure 2.2, the
first ORF ends at position 9 (sub-ET 1 ); the second ORF ends at position 6
(sub-ET 2 ); and the last ORF ends at position 2 (sub-ET 3 ).