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equal to or greater than
R
, or into 0 otherwise. For this problem we are going
to use a rounding threshold of 0.5.
For evaluating the fitness we will use equation (3.14), which is based both
on the sensitivity and specificity. Thus, for this problem,
f
max
= 1000.
For this problem, chromosomes composed of three genes with an
h
= 7
and sub-ETs linked by addition were used. The parameters used per run are
summarized in Table 4.5. Note that the number of generations is not shown,
as in real-world situations one usually performs several dozens of runs until
a good solution has been found. Also note that small populations of 30 indi-
viduals were used, as this allows a quick and efficient evolution.
Given the complexity of the problem, I used the software Automatic Prob-
lem Solver (APS) by Gepsoft to model this function because it reflects more
accurately the effort and strategies that go into solving a complex real-world
problem. For one, it allows the easy optimization of intermediate solutions
and, for another, it also allows the easy checking of the evolved models against
Table 4.5
Settings used in the breast cancer problem.
Population size
30
Number of training samples
350
Number of testing samples
174
Function set
+ + - - * * / LT GT LOE GOE ET NET
Terminal set
d0 - d8
Head length
7
Gene size
15
Number of genes
3
Linking function
+
Chromosome length
45
Mutation rate
0.044
Inversion rate
0.1
IS transposition rate
0.1
RIS transposition rate
0.1
One-point recombination rate
0.3
Two-point recombination rate
0.3
Gene recombination rate
0.3
Gene transposition rate
0.1
Fitness function
Equation (3.14)
Rounding threshold
0.5
