Information Technology Reference
In-Depth Information
[ 4] = f(1.15833) = -0.118934
[ 5] = f(0.689667) = 1.21997
[ 6] = f(1.71039) = 0.451673
[ 7] = f(1.46631) = 2.27802
[ 8] = f(-0.2294) = 1.18301
[ 9] = f(0.701203) = 0.973505
[10] = f(0.061004) = 1.05739
[11] = f(0.317169) = 0.837101
[12] = f(1.04767) = 2.04486
[13] = f(0.425842) = 1.30897
[14] = f(0.843506) = 1.82601
[15] = f(-0.049316) = 1.0493
[16] = f(-0.2294) = 1.18301
[17] = f(-0.642487) = 1.62467
[18] = f(-0.916901) = 0.535716
[19] = f(-0.065002) = 1.05792
As you can see, the best of this generation is considerably better than the
best of the initial population. In this case, the parameter value
x
0
= 1.46631
was discovered, resulting in
f
(
x
0
) = 2.27802.
It is worth pointing out that, even though this is an evolutionary process
where most of the times some kind of learning takes place, for this simple
problem of just one parameter, the system benefits little from past experi-
ence and each new best-of-generation individual is just a lucky winner that
suffered a very beneficial mutation. Note, however, that for multidimensional
optimization problems, past experience counts, as some genes might just be
too precious to lose and are passed on from generation to generation.
Then for the next five generations there was no improvement in best out-
put and all the best individuals of these populations are either clones of the
best created by elitism or variants of the best created mostly by replacing old
random constants by new ones (all these individuals are shown in bold):
GENERATION N: 2
Structures:
?2-[ 0]-{-0.684418, -0.401642, 1.46631, 1.53787, 0.160522}
?3-[ 1]-{1.05344, 0.05429, 1.17279, 0.677033, 0.701203}
?1-[ 2]-{1.05344, -0.275757, 1.41119, -0.014373, 0.843506}
?4-[ 3]-{-0.850556, -0.275757, 1.98966, 1.17444, 1.72028}
?4-[ 4]-{-0.850556, 1.1875, 1.74033, -0.825592, 0.061004}
?3-[ 5]-{0.644684, -0.065002, 1.2999, 1.17444, -0.805512}
?0-[ 6]-{0.769379, 0.231598, 1.28174, -0.642487, 0.620331}
?3-[ 7]-{0.769379, 0.231598, -0.444427, 1.40485, -0.006225}
?4-[ 8]-{1.47241, 1.2999, -0.065002, 1.74732, 0.160522}
?4-[ 9]-{1.31094, -0.531799, -0.709107, -0.916901, -0.101165}
