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selection range or they returned calculation errors such as division by zero.
And as you can easily check by drawing their expression trees, in this par-
ticular case, it was a division by zero that caused all these individuals to die
without leaving offspring: indeed, all the six unviable chromosomes code
for programs where a division by zero took place and therefore were labeled
unfit to reproduce.
It is worth pointing out that, in gene expression programming, all calcula-
tion errors are handled similarly: every time a program gives a calculation
error (divisions by zero, square roots or logarithms of negative numbers, and
so forth) it is made unviable. This means that it will not be able to pass on its
genes to the next generation. This is a good alternative to the creation of
useless programs with dubious protected mathematical operators as is usu-
ally done in genetic programming.
As shown in the initial population above, the best individual of this gen-
eration, chromosome 16, has fitness 886.7593. Let's now analyze its per-
formance more closely. Table 3.4 compares the results predicted by this pro-
gram with the target value. Note that none of the fitness cases was solved
within the chosen precision of 0.01. However, in all cases, the absolute error
was within the chosen selection range of 100.
The expression of the best individual of this generation and the corre-
sponding mathematical expression is shown in Figure 3.31. Note that gene 3
contributes nothing to the overall solution as the whole sub-ET encodes zero,
and therefore may be considered a neutral gene. Note also the creation of
Table 3.4
Fitness evaluation of a model (best program of generation 0).
Target
Model
Error
Fitness
44.91
33.0282
11.8818
88.1182
7.341
25.0737
17.7327
82.2673
-4.477
3.09508
7.57208
92.42792
-2.307
9.88206
12.18906
87.81094
73.494
56.5148
16.9792
83.0208
17.41
38.6496
21.2396
78.7604
16.073
36.9019
20.8289
79.1711
-0.419
1.86705
2.28605
97.71395
3.147
3.32539
0.17839
99.82161
8.897
6.54412
2.35288
97.64712
