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plots. Indeed, not only the h chosen was not the most advantageous (see
Figure 4.1), but also single-gene chromosomes were used. Remember, though,
that, for most problems, the multigenic system of gene expression program-
ming is much more efficient than the unigenic one, as most problems are
better modeled by using multiple, smaller building blocks or terms.
Suppose that, after the analyses shown in Figures 4.1 and 4.2, we were
unable to find a satisfactory solution to the problem at hand or the system
was not evolving efficiently. Then we could try a multigenic system and also
try different ways of linking the sub-ETs. For instance, we could start by
choosing multiple genes with a head length of six, encoding sub-expression
trees linked by addition. Figure 4.3 shows such an analysis for this problem.
In this experiment, the mutation rate was equivalent to two one-point muta-
tions per chromosome and, therefore, varies according to chromosome length,
p 1r = p 2r = p gr = 0.3, and p i = p is = p ris = p gt = 0.1.
It is worth pointing out that gene expression programming can cope very
well with an excess of genes: the success rate for the 10-genic system is still
very high (59%). Again we can see that a certain amount of redundancy
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Figure 4.3. Variation of success rate with the number of genes. For this analysis
G = 50, P = 30, h = 6 (a gene length of 13), and the sub-ETs were linked by
addition. The success rate was evaluated over 100 identical runs.
 
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