Information Technology Reference
In-Depth Information
[0] = f(1.648345947) = 2.64612100283072
[3] = f(1.843414307) = 2.80410042875014
[13] = f(1.852813721) = 2.84557968213877
[119] = f(1.848297119) = 2.84565284514179
[152] = f(1.850646973) = 2.85026471989876
[1400] = f(1.850463868) = 2.85026738184542
[2692] = f(1.850585938) = 2.85027241426006
[6416] = f(1.85055542) = 2.85027370872288
It was generated using the same settings of Table 8.1, with the difference that
the number of generations was increased to 50,000. And as you can see,
although a pretty good solution with an output higher that 2.85 was discov-
ered early on in generation 152, the algorithm continued its search for the
global optimum and three better approximations were discovered. And the
best of all, discovered in generation 6416, is indeed a very good approxima-
tion to the global maximum of function (8.4).
8.2 The GEP-PO Algorithm
The GEP-PO algorithm is considerably more complex than either the HZero
algorithm or the GA as it explores the GEP-RNC algorithm in all its com-
plexity, making good use of its complex genes for fine-tuning the multiple
parameters that optimize a function. Indeed, thanks to these sharp tools, the
GEP-PO algorithm is rarely stuck in local optima for long stretches of time
and is, therefore, always on the move to find the elusive global optimum.
8.2.1 The Architecture
Similarly to the HZero algorithm, the GEP-PO algorithm also uses
N
different
genes to encode the values of the
N
parameters that optimize a function. But
here the genes are much more complex than the simple structures of the
HZero algorithm and the parameters are designed rather than just found.
Consider, for instance, the chromosome below composed of two genes:
Gene 1: +/+??+???????4374796
C
1
: {-0.698, 0.781, -0.059, -0.316, -0.912,
0.398, 0.157, 0.473, 0.103, -0.756}
Gene 2: +////+???????4562174
C
2
: {0.104, 0.722, -0.547, -0.052, -0.876,
-0.248, -0.889, 0.404, 0.981, -0.149}
(8.5a)
