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phenotype systems, and full-fledged genotype/phenotype systems. And the
mechanisms of genetic modification of all these systems are intricately con-
nected with their representation schemes.
We have already seen that gene expression programming uses not only
mutation and recombination but also different kinds of transposition and,
therefore, can be useful for conducting a rigorous analysis of the power of
different search operators in order to gain some insights into their role in
evolution. We will see that mutation is by far the single most important ge-
netic operator, outperforming recombination considerably. In fact, all three
kinds of genetic recombination analyzed here (one-point, two-point, and gene
recombination) perform considerably worse than mutation and also consid-
erably worse than simple intrachromosomal transposition mechanisms. In
addition, we are also going to analyze with great detail the evolutionary dy-
namics produced by all these genetic operators in order to understand their
importance in evolution.
12.1.1 Their Performances
For this analysis of the genetic operators and their power, the following rela-
tively complex test sequence was chosen:
4
3
2
a
n
5
n
4
n
3
n
2
n
1
(12.1)
where
n
consists of the nonnegative integers. This sequence was chosen for
four reasons: (1) it can be exactly solved and therefore provide an accurate
measure of performance in terms of success rate; (2) it requires relatively
small populations and relatively short evolutionary times, making the task
feasible; (3) it provides sufficient resolution to allow the comparison of dis-
similarly performing operators such as mutation and gene recombination;
and (4) it is appropriate to study all the genetic operators, including opera-
tors specific of multigenic systems like gene recombination.
In all the experiments of this section, the first 10 positive integers
n
and
their corresponding term
a
n
were used as fitness cases (Table 12.1); the fit-
ness function was evaluated by equation (3.3b) and a selection range of 20%
Table 12.1
Set of fitness cases for the sequence induction problem.
n
1
2
3
4
5
6
7
8
9
10
a
n
15
129
547
1593
3711
7465
13539
22737
35983
54321
