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Table 6.4
Planetary data used to rediscover Kepler's Third Law.
Planet
Distance
Orbital Period
Venus
0.72
0.61
Earth
1.00
1.00
Mars
1.52
1.84
Jupiter
5.20
11.9
Saturn
9.53
29.4
Uranus
19.1
83.5
In this study, we are going to use three different algorithms to solve the
orbital period problem. The first one consists of the basic gene expression
algorithm with just one gene (UGS); the second consists again of the basic
GEA, but a multigenic system composed of two genes with the sub-ETs linked
by multiplication will be used (MGS); and the last one consists of the cellu-
lar system with two ADFs (MCS). For all the experiments, in the function set
we will use the basic arithmetical operators plus the square root function
“Q”, thus giving F = {+, -, *, /, Q} (and, in the cellular system, the same
function set will be used in the homeotic genes, that is, F
H
= {+, -, *, /, Q});
the terminal set will consist obviously of the independent variable
D
, which
will be represented by “a”, thus giving T = {a}. This study, with its three
different experiments, is summarized in Table 6.5.
And as you can see in Table 6.5, in all the experiments, the discovery of
Kepler's Third Law was an easy task for gene expression programming. In-
deed, using populations of just 10 individuals evolving for just 50 genera-
tions, the unigenic system discovered Kepler's Third Law in 76 out of 100
runs; the multigenic system in 96% of the runs; and the multicellular system
in 99% of the runs. Let's now analyze some of the perfect solutions discov-
ered in the three experiments.
The first 10 perfect solutions discovered in the UGS experiment are shown
below (the numbers in square brackets indicate, respectively, the run and the
generation by which they were created; and the number in parentheses after
the fitness indicates the program size):
012345678901234
Q*a*/a*aaaaaaaa-[01,01] = 6 (10)
/*/aaaQaaaaaaaa-[04,25] = 6 (8)
*Q**Q/aaaaaaaaa-[05,15] = 6 (11)
