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In-Depth Information
Table 3.2
Set of 10 random computer generated fitness cases
used in the simple problem of symbolic regression.
a
f(a)
6.9408
44.909752
-7.8664
7.3409245
-2.7861
-4.4771234
-5.0944
-2.3067443
9.4895
73.493805
-9.6197
17.410214
-9.4145
16.072905
-0.1432
-0.41934688
0.9107
3.1467872
2.1762
8.8965232
selection range and a precision for the error equal to 0.01. Thus, for the 10
fitness cases of Table 3.2
f
max
= 1000.
The second major step is to choose the set of terminals
T
and the set of
functions
F
. For this problem, the terminal set consists obviously of the inde-
pendent variable, giving T = {a}. The choice of the appropriate function set
is not so obvious, but a good guess can be done so that all the necessary
mathematical operators are included. For this problem, we will make things
simple and use the four arithmetic operators, thus giving F = {+, -, *, /}.
The third major step is to choose the chromosomal architecture: the length
of the head and the number of genes. In this problem we will use an
h
= 7 and
three genes per chromosome.
The fourth major step is to choose the kind of linking function. In this case
we will link the sub-ETs by addition.
And finally, the fifth major step in preparing to use gene expression pro-
gramming is to choose the set of genetic operators and their rates. In this
case we will use a combination of all the modification operators introduced
in the previous section (mutation, inversion, the three kinds of transposition,
and the three kinds of recombination).
The parameters used per run are summarized in Table 3.3. For this prob-
lem, a small population of 20 individuals was chosen so that all the individu-
als created in the evolutionary process could be completely analyzed, with-
out however filling this topic with pages and pages of encoded individuals.
