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The expression of this perfect solution is shown in Figure 8.8. It encodes
the parameter value
x
0
= 1.85019, giving
f
(
x
0
) = 2.85016, thus very close to
the global maximum of function (8.4). Note that this individual is a direct
descendant of the best individual of the previous generation. As you can see
by comparing both solutions, this new individual was created thanks to a
mutation in the array of random constants (the constant 1.5076 at position 0
was replaced by 1.49054). It is worth pointing out that this kind of learning is
a.
01234567890123456
+?/+/??????210412
C = {1.49054, -0.039703, 1.41498, 0.660401, -0.132354}
b.
ET
1.41498
-0.039703
1.49054
-0.132354
-0.039703
f
(1.85019)
(2.85016)
c.
Figure 8.8.
Perfect solution designed in generation 6 (chromosome 12) encoding
the parameter value for the global maximum of function (8.4).
a)
The chromosome
of the individual with its random numerical constants.
b)
The expression tree
encoded in the chromosome.
c)
The parameter value represented by the expression
tree and corresponding function value.
not possible with the HZero algorithm as each parameter is expressed using
just one node.
As we did before for the HZero algorithm, let's now see how close the
GEP-PO algorithm can get to the global maximum of function (8.4) by letting
it run for a few thousands of generations until no further improvement is
observed. Consider, for instance, the evolutionary history presented below
(the number in square brackets indicates the generation by which these solu-
tions were discovered):
