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classification problems. So, for this problem, the fitness function will be
therefore evaluated by equation (3.14).
Suppose we were again interested in finding a parsimonious solution to a
higher order exactly-one-on function (say, 11-exactly-one-on function) in
terms of ANDs, ORs, and NOTs. Again, we could try the direct approach,
but as for the odd-parity functions, we would soon find out that these func-
tions are also hard to design (Table 4.16). In fact, I was unable to find a
perfect solution to the 9-exactly-one-on function using this approach. And
indeed, not even the use of XOR in the function set could help me in finding
a perfect solution to the problem at hand. The only alternative then consists
of using UDFs as a way of identifying some underlying pattern in their de-
sign (Table 4.17).
And as you can see in Table 4.17, the use of lower order exactly-one-on
functions as UDFs in the design of higher order exactly-one-on functions
results in a much better performance (compare Tables 4.16 and 4.17), which
Table 4.16
Parameters for the
n
-exactly-one-on problem without UDFs.
2-1On
3-1On
4-1On
5-1On
6-1On
Number of runs
100
100
100
100
100
Number of generations
50
1,000
10,000
10,000
100,000
Population size
20
30
30
30
30
Number of fitness cases
4
8
16
32
64
Function set
A O N
A O N
A O N
A O N
A O N
Terminal set
a b
a b c
a b c d
a b c d e
a b c d e f
Head length
10
10
10
10
10
Gene length
21
21
21
21
21
Number of genes
2
2
2
4
4
Linking function
A
A
A
A
A
Chromosome length
42
42
42
84
84
Mutation rate
0.044
0.044
0.044
0.044
0.044
Inversion rate
0.1
0.1
0.1
0.1
0.1
IS transposition rate
0.1
0.1
0.1
0.1
0.1
RIS transposition rate
0.1
0.1
0.1
0.1
0.1
One-point recombination rate
0.3
0.3
0.3
0.3
0.3
Two-point recombination rate
0.3
0.3
0.3
0.3
0.3
Gene recombination rate
0.3
0.3
0.3
0.3
0.3
Gene transposition rate
0.1
0.1
0.1
0.1
0.1
Fitness function
Eq. (3.14)
Eq. (3.14)
Eq. (3.14)
Eq. (3.14)
Eq. (3.14)
Success rate
98%
85%
50%
38%
39%
