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Table 5.2
Set of 10 random computer generated fitness cases used in
the polynomial function problem with rational coefficients.
f
(x)
x
-8.5013
169.7278883
-0.8696
-0.676572453
3.7181
49.25514232
5.0878
86.34118911
-4.313
37.01043094
1.9775
16.84126999
-8.767
181.3638583
-5.5617
66.60191701
-1.4234
1.035098188
6.9014
151.1379353
an average best-of-run fitness of 934.534 and an average best-of-run R-
square of 0.999919082).
It is also interesting to take a look at the best-of-experiment solutions dis-
covered with both systems (see Figures 5.1 and 5.2). The one designed using
the simpler approach was found in generation 395 of the second run, and has
an R-square of 0.999994826 and a fitness of 896.542. Its chromosome is
shown below (the sub-ETs are linked by addition):
01234567890120123456789012
/x-/-+xxxxxxx*++x/+xxxxxxx
(5.2a)
And as you can see in Figure 5.1, it codes for the following function:
2
(5.2b)
y
3
x
3
.
5
x
which is a slightly simplistic approximation to the target function (5.1). Cu-
riously enough, this solution was found in 71 out of 100 runs, which sug-
gests that this solution is a strong attractor in the particular fitness landscape
explored in this experiment. This is perhaps the reason why the algorithm
performed so poorly, and therefore a different fitness function or a different
function set or a different chromosome structure would most probably be
more appropriate to solve this particular problem.
The best-of-experiment solution designed with the GEP-NC algorithm was
found in generation 63 of run 25 and has an R-square of 0.9999999999082
