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As you can see in Figure 4.6, for the next four generations no improve-
ment in best fitness was observed. But in generation 6 a better solution with
fitness 990 was created:
0123456789012012345678901201234567890120123456789012
+-/-a-aaaaaaa+-a**aaaaaaaa*+-a*aaaaaaaa+*a+a*aaaaaaa
(4.4a)
As its expression shows, three of the terms of this intermediate solution match
exactly the target function (4.1); in this case, only the last term is missing
(the contribution of each gene is shown in brackets):
3
2
y
(
a
)
(
a
)
(
0
(
a
a
a
)
(4.4b)
For the next 12 generations no improvement in best fitness occurred (see
Figure 4.6). But in generation 19 a perfect solution with maximum fitness
was found:
0123456789012012345678901201234567890120123456789012
+*a/-aaaaaaaa*-/++aaaaaaaa-/***-aaaaaaa+***/*aaaaaaa
(4.5a)
As its expression shows, it matches exactly the target function (4.1) (the
contribution of each gene is shown in brackets):
y
(
a
)
(
0
(
(
a
3
a
2
)
(4.5b)
The detailed analysis of these best-of-generation programs shows that some
of their components are redundant or neutral, like the addition/subtraction of
zero or the multiplication/division by one. However, the existence of these
redundant clusters, be they small neutral clusters in the sub-ETs or entire
neutral genes like gene 3 in chromosome (4.4) above or gene 2 in chromo-
some (4.5), is important to the evolution of fitter individuals (compare, in
Figures 4.1 and 4.3, the success rate of a compact unigenic system with a
head length of six with other less compact systems, either with more genes
or head lengths greater than six).
In summary, gene expression programming is a very flexible system, with
easily navigable solution spaces. Consequently, default settings can be used
to solve most problems, needing just small adjustments here and there to
make the most of any problem. Thus, small populations of just 30 individu-
als (evolving for as long as necessary as GEP populations never become
stagnant) undergoing the typical degree of genetic modification (see, for in-
stance, Table 4.1); a chromosome architecture of three genes with
h
= 10
