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plication of two constants. We will also use small populations of just 20 indi-
viduals so that we can analyze the evolutionary process in its entirety and still
keep a readable presentation. The complete list of parameters used per run is
given in Table 8.1. And as you can see, for this simple chromosomal struc-
ture, we can only benefit from mutation, both of the gene sequence and the
random constants themselves, and from one-point recombination (it still works
because the RNCs stay in the same place). Note, however, that for multidi-
mensional optimization problems, we can also benefit from two-point recom-
bination, gene recombination, and gene transposition for fine-tuning the pa-
rameters. Let's see then how these structures evolve, finding good solutions
to the problem at hand.
Table 8.1
Settings for the simple optimization problem using the HZero algorithm.
Number of generations
50
Population size
20
Terminal set
?
Random constants array length
5
Random constants type
Rational
Random constants range
[-1, 2]
Head length
0
Gene length
2
Number of genes
1
Chromosome length
2
Random constants mutation rate
0.55
Dc-specific mutation rate
0.2
One-point recombination rate
0.3
The evolutionary dynamics of the successful run we are going to analyze is
shown in Figure 8.1. And as you can see, in this run, the global maximum of
function (8.4) was found in generation 8.
Both the structures and the outputs of all the individuals of the initial
population are shown below (the best of generation is shown in bold):
GENERATION N: 0
Structures:
?1-[ 0]-{0.317169, -0.356384, 0.231598, -0.356384, -0.916901}
?1-[ 1]-{1.95847, 0.743866, 1.47241, 0.06842, -0.480194}
?4-[ 2]-{-0.72638, -0.827637, 0.578095, 1.4209, 1.32874}
?3-[ 3]-{0.769379, 0.231598, 1.28174, -0.642487, -0.808625}
