Information Technology Reference
In-Depth Information
As you can see, the GEP-PO algorithm can approximate the parameter val-
ues with much more precision and, therefore, can find much better solutions
than either the HZero algorithm or the GA.
It is also interesting to find out how close can these systems get to the
global maximum by allowing evolution to take its course for several thou-
sands of generations. For instance, running the HZero algorithm for 100,000
generations (three orders of magnitude longer than in the experiment sum-
marized in the first column of Table 8.3), the following solutions were dis-
covered (the number in square brackets indicates the generation by which
they were created):
[0] = f(9.126373291, 9.266235351) = 11.6629777173885
[3] = f(8.857421875, 5.656158447) = 12.694624653527
[4] = f(5.900817871, 8.469024658) = 14.6762045169257
[5] = f(9.068511962, 5.491333008) = 15.0123472145664
[7] = f(9.068511962, 8.772583008) = 18.2818098478718
[14] = f(9.068511962, 8.751739502) = 18.3572449335579
[21] = f(9.050445556, 8.751739502) = 18.4108930891067
[31] = f(9.050445556, 8.708007813) = 18.5147538223188
[75] = f(9.050445556, 8.693634033) = 18.5327871603454
[92] = f(9.03729248, 8.693634033) = 18.5420822284372
[100] = f(9.03729248, 8.655212402) = 18.5512882545018
[256] = f(9.03729248, 8.66192627) = 18.5537607892668
[914] = f(9.037872314, 8.66192627) = 18.5538790786118
[946] = f(9.037872314, 8.663665772) = 18.5542384233189
[1148] = f(9.037872314, 8.66381836) = 18.5542644183508
[1724] = f(9.037872314, 8.664001465) = 18.5542944354892
[1833] = f(9.037872314, 8.668609619) = 18.554626996419
[2247] = f(9.038848876, 8.668609619) = 18.5547162111929
[5005] = f(9.038848876, 8.667785645) = 18.554716485223
[18408] = f(9.038848876, 8.668457031) = 18.5547182253551
[21950] = f(9.038848876, 8.668334961) = 18.554719194082
[41957] = f(9.038848876, 8.66809082) = 18.5547194180098
[63082] = f(9.038848876, 8.668273926) = 18.5547194642522
[63489] = f(9.039001464, 8.668273926) = 18.5547209319945
[72426] = f(9.039001464, 8.668243408) = 18.5547210135332
As you can see, the HZero algorithm is able to find the global maximum of
function (8.7) with great precision.
And running the GEP-PO algorithm for 1,000,000 generations (also three
orders of magnitude longer than in the experiment summarized in the second
column of Table 8.3), the following solutions were designed (the generation
by which they were created is in square brackets):