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[0] = f(0.8662827398) = 1.75539246128292
[1] = f(1.243607008) = 2.2186092614651
[2] = f(1.442756154) = 2.405557613831
[3] = f(1.643576457) = 2.61022348179365
[7] = f(1.84369) = 2.80758281206205
[35] = f(1.851014) = 2.85007488485697
[164] = f(1.850769) = 2.85022892534645
[226] = f(1.850495) = 2.85027125170459
[526] = f(1.850586) = 2.85027240989802
[1894] = f(1.850525) = 2.85027330541754
[14604] = f(1.850565877) = 2.85027345685206
[14616] = f(1.850542097) = 2.85027374018891
[14636] = f(1.850545429) = 2.85027376273599
[14651] = f(1.850548264) = 2.85027376594376
[14784] = f(1.850547275) = 2.85027376649316
[14952] = f(1.850547484) = 2.85027376652619
[28863] = f(1.850547459) = 2.85027376652646
[41270] = f(1.85054747) = 2.85027376652649
[49986] = f(1.850547466) = 2.8502737665265
It was generated using the same settings of Table 8.2, with the difference that
the number of generations was increased a thousand times. And as you can
see, although a very good solution was discovered early on in generation 35,
the algorithm continued its search for the global maximum and a total of 13
better approximations were made, considerably more than the additional three
approximations achieved by the HZero algorithm (see page 312). This clearly
shows the advantages of a hierarchical learning process where the parameter
values are designed rather than just discovered; that is, in the GEP-PO sys-
tem, from generation to generation very good solutions are selected to repro-
duce with modification and, by changing slightly their structures, it is possi-
ble to create even better solutions that will get closer and closer to the global
maximum. As a comparison, this kind of learning is totally absent in the
HZero system as it cannot learn and change at the same time with just one
node to express the solution.
It is also worth noticing that the best approximation to the global maxi-
mum of function (8.4) designed by the GEP-PO algorithm in this experi-
ment,
f
(1.850547466) = 2.8502737665265, is closer to the global maximum
than the best solution discovered by the HZero algorithm in similar circum-
stances,
f
(1.85055542) = 2.85027370872288.
Let's now see how both these algorithms perform in two complex optimi-
zation problems of two and five parameters.
