Evolutionary Studies - Gene Expression Programming - page 440

zation with g = 13. The same is observed in the sequence induction experi-
ment, where the success rate of the most redundant organization ( g = 169) is
16% compared to 1% for the most compact organization ( g = 29).
The structural analysis of compact organizations and less compact ones
can also be useful for understanding the role of redundancy in evolution. For
instance, the following perfect solutions to the function (4.1) were discov-
ered using, respectively, head lengths of 6, 18, and 48 (only the K-expres-
sions are shown):
(a) 0123456789012
*++*//aaaaaaa
(b) 012345678901234567890123456
+-*+/+a*/**a*/a++-aaaaaaaaa
(c) 0123456789012345678901234567890123456789...
/+aa++*+aa+*-a--+-*+*+/**a*a-*--+*/-/-/a...
...0123456789012345678901234567890123456
...aa//-/*-aaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Note that the first solution with an h = 6 is expressed using 13 nodes, and
therefore the entire gene was used for its expression; the second solution
with an h = 18 is expressed using 31 nodes, and therefore has a noncoding
region with six elements; and the last solution with an h = 48 uses for its
expression only 77 of the 97 elements of the gene and therefore has a
noncoding region with 20 elements. Note also that not only the length of the
noncoding region increases from the most compact to the less compact (0, 6,
and 20, respectively) but also increases the number of redundant or neutral
motifs. For instance, two neutral motifs using a total of 14 nodes can be
counted on the medium compact solution and seven neutral motifs involving
38 nodes can be counted on the less compact one. This phenomenon is known
as code bloat in genetic programming and many have argued about its evolu-
tionary function (Angeline 1994, 1996; Nordin et al. 1995). Like all kinds of
genetic redundancy, neutral motifs are most probably beneficial whenever
used in good measure. This can be rigorously evaluated using gene expres-
sion programming, although such an analysis would require lots of time.
However, what was learned from the analysis shown in Figure 12.11 (and
also from Figure 12.12 in the next section) and what is known about the
evolution of proteins or technological artifacts suggest an important role for
neutral regions in evolution. Their nonexistence or their excess results most