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2.748801579 against 2.748712187. And the reason for this superiority resides
obviously in the fine-tuning capabilities of the GEP-PO algorithm.
Consider, for instance, the best-of-experiment solution created with the
HZero algorithm in generation 10399 of run 97:
f
(
p
1
,
p
2
,
p
3
,
p
4
,
p
5
) = (1.21496582, 7.75982666, 0.558441162, 0.572570801, 9.826141358)
for which the function value at this point is:
f
(
p
1
,
p
2
,
p
3
,
p
4
,
p
5
) = 2.74912071753426
Consider now the parameter values for the best-of-experiment solution
designed by the GEP-PO algorithm in generation 14834 of run 10:
f
(
p
1
,
p
2
,
p
3
,
p
4
,
p
5
) = (0, 1.571259, -0.548713482, -0.5760533165, -9.9444807)
And the function value at this point is:
f
(
p
1
,
p
2
,
p
3
,
p
4
,
p
5
) = 2.7491281426491
which is slightly higher than the best solution discovered with the HZero
algorithm.
As we did for the two-parameter function (8.7) above, let's see what kind
of heights can be reached by letting these systems evolve for a considerable
amount of time. For instance, running the HZero algorithm for 2,000,000
generations (two orders of magnitude longer than in the experiment summa-
rized in the first column of Table 8.4), the following solutions were discov-
ered (the number in square brackets indicates the generation in which they
were discovered):
[0] = f(-1.037597656, -1.38204956, -2.631988526, -9.757141114, -7.959350586) = 2.58443976787767
[12] = f(7.128662109, -3.721313477, -7.474395752, -3.179992675, 8.333435058) = 2.63238917644785
[17] = f(1.474212646, 7.459075928, -2.71975708, -0.615753174, 5.488342285) = 2.67447123876539
[24] = f(1.474212646, 7.459075928, -2.71975708, -0.615753174, 9.441009521) = 2.70166476215306
[29] = f(7.459075928, 2.636352539, -2.71975708, -0.615753174, 9.441009521) = 2.73115091447637
[51] = f(-6.700866699, 4.013244628, -2.71975708, -0.615753174, 9.441009521) = 2.73185409502974
[111] = f(4.85131836, -6.269958496, 1.468261719, -2.069793701, -3.105651855) = 2.73837389558143
[247] = f(-6.269958496, 4.85131836, 1.248565674, -2.069793701, 3.654327393) = 2.73907137151942
[398] = f(1.624511719, -7.610443115, 1.248565674, -2.069793701, 3.654327393) = 2.73918633590436
[431] = f(1.902191163, -7.610443115, 1.248565674, -2.069793701, 3.654327393) = 2.74173170877181
[1004] = f(1.902191163, -7.610443115, 1.248565674, 0.693542481, 3.654327393) = 2.74683021639669
[1966] = f(1.902191163, -7.610443115, 0.593597412, -0.666992188, 8.001739501) = 2.74842158975813
[2200] = f(-7.610443115, 1.902191163, 0.593597412, -0.666992188, -7.920471192) = 2.74883995593118
[2811] = f(0.782867432, -7.819946289, 0.593597412, -0.666992188, -7.920471192) = 2.74887152265203
[2846] = f(1.358184814, 0.782867432, 0.593597412, -0.666992188, -7.920471192) = 2.74887936230107
