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Table 5.9
Performance and settings used in the breast cancer problem.
GEA-B
GEP-NC
GEP-RNC
Number of runs
100
100
100
Number of generations
1000
1000
1000
Population size
30
30
30
Number of fitness cases
350
350
350
Function set
4(+ - * /)
4(+ - * /)
4(+ - * /)
Terminal set
d0-d8
d0-d8, c0-c4
d0-d8 ?
Random constants array length
--
--
10
Random constants type
--
--
Rational
Random constants range
--
--
[-2, 2]
Head length
7
7
7
Gene length
15
15
23
Number of genes
3
3
3
Linking function
+
+
+
Chromosome length
45
45
69
Mutation rate
0.044
0.044
0.044
Inversion rate
0.1
0.1
0.1
IS transposition rate
0.1
0.1
0.1
RIS transposition rate
0.1
0.1
0.1
One-point recombination rate
0.3
0.3
0.3
Two-point recombination rate
0.3
0.3
0.3
Gene recombination rate
0.3
0.3
0.3
Gene transposition rate
0.1
0.1
0.1
Dc-specific mutation rate
--
--
0.044
Dc-specific inversion rate
--
--
0.1
Dc-specific transposition rate
--
--
0.1
Random constants mutation rate
--
--
0.01
Fitness function
Eq. (3.10)
Eq. (3.10)
Eq. (3.10)
Rounding threshold
0.5
0.5
0.5
Average best-of-run fitness
339.340
339.050
339.130
Furthermore, a set of random numerical constants represented by the numer-
als 0-9 was used, that is, R = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, and the ephemeral
random constant “?” ranged over the integer interval [0, 3] (the complete list
of all the parameters used per run is shown in Table 5.6).
As shown in Table 5.6, the probability of success using the GEA-B algo-
rithm is 97%, considerably higher than the 35% obtained using the GEP-NC
algorithm or the 75% obtained using the GEP-RNC algorithm, showing that,
for this kind of problem, the inclusion of numerical constants in the evolu-
tionary toolkit results in worse performance. Thus, when the required con-
stants to solve a problem are small integer constants, evolutionary algorithms
