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probably in an inefficient evolution whereas their existence in good measure,
as shown here, is extremely beneficial.
12.4.2 Genetic Neutrality in Multigenic Systems
Another way of analyzing genetic neutrality in gene expression programming,
consists of increasing the number of genes. For that purpose a compact,
unigenic system capable of exactly solving the problem at hand is chosen as
the starting point. Thus, for the function finding problem, the starting point is a
unigenic system with a head length of six (gene length equal to 13), and a
head length of 14 (gene length equal to 29) for the sequence induction prob-
lem (see Figure 12.11).
As shown in Figure 12.12, the results obtained for multigenic systems
further reinforce the importance of neutrality in evolution. Note that, in both
experiments, the efficiency of the system increases dramatically with the
introduction of a second gene and that compact unigenic systems are much
less efficient than less compact, multigenic ones. For instance, in the func-
tion finding problem, the compact, unigenic system (chromosome length
c
equal to 13) has a success rate of 2% whereas the success rate in the two-
genic system (
c
= 26) is 94%. In the sequence induction problem, the success
100
90
80
70
FF
SI
60
50
40
30
20
10
0
0
1
2
3
4
5
6
7
8
9
10
Number of genes
Figure 12.12.
Variation of success rate with the number of genes for the function
finding (FF) and sequence induction (SI) problems. The success rate was evalu-
ated over 100 independent runs.
