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easily evolved using a special domain Dc for handling random numerical
constants. As for the GEP-RNC algorithm, the Dc comes after the tail but, in
this case, has a length equal to 6
h
in order to cover for all the cases, including
when all the nodes in the head are function nodes requiring the maximum
value of six coefficients.
Consider, for instance, the chromosome below with a head length of two
(the Dc is shown in bold):
01234567890123456
FFabc
252175089728
(7.2)
where the numerals 0-9 represent the polynomial coefficients. Then, for the
set of random numerical constants:
C = {-0.606, -0.398, -0.653, -0.818, -0.047, 0.036, 0.889, 0.148, -0.377, -0.841}
its expression gives:
y
0
606
0
.
377
y
0
.
841
a
0
148
y
a
0
653
y
2
1
0
.
377
a
2
(7.3)
1
1
where
2
2
.
y
0
.
653
0
036
b
0
653
c
0
398
bc
0
148
b
0
.
036
c
1
Table 7.1
Bivariate basis polynomials.
F
a
a
x
a
x
a
x
x
1
0
1
1
2
2
3
1
2
F
a
a
x
a
x
2
0
1
1
2
2
2
1
2
2
F
a
a
x
a
x
a
x
a
x
3
0
1
1
2
2
3
4
F
a
a
x
a
x
x
a
x
2
1
4
0
1
1
2
1
2
3
2
2
F
a
a
x
a
x
5
0
1
1
2
2
1
F
a
a
x
a
x
a
x
6
0
1
1
2
2
3
F
a
a
x
a
x
2
1
a
x
2
2
7
0
1
1
2
3
F
a
a
x
2
1
a
x
2
2
8
0
1
2
2
1
2
2
F
a
a
x
a
x
a
x
x
a
x
a
x
9
0
1
1
2
2
3
1
2
4
5
F
a
a
x
a
x
a
x
x
a
x
2
1
10
0
1
1
2
2
3
1
2
4
2
1
2
2
F
a
a
x
a
x
x
a
x
a
x
11
0
1
1
2
1
2
3
4
F
a
a
x
x
a
x
2
1
a
x
2
2
12
0
1
1
2
2
3
2
2
F
a
a
x
a
x
x
a
x
13
0
1
1
2
1
2
3
F
a
a
x
a
x
x
14
0
1
1
2
1
2
F
a
a
x
x
15
0
1
1
2
2
1
F
a
a
x
x
a
x
16
0
1
1
2
2
