Information Technology Reference
In-Depth Information
Table 4.15
Parameters for the odd-
n
-parity problem with UDFs.
Odd-3
Odd-4
Odd-5
Odd-6
Number of runs
100
100
100
100
Number of generations
1000
1000
1000
1000
Population size
30
30
30
30
Number of fitness cases
8
16
32
64
Function set
A O N
A O N
A O N
A O N
User defined functions
Odd-2
Odd-3
Odd-4
Odd-5
Terminal set
a b c
a b c d
a b c d e
a b c d e f
Head length
7
7
7
7
Gene length
15
15
15
15
Number of genes
2
2
2
2
Linking function
A
A
A
A
Chromosome length
30
30
30
30
Mutation rate
0.044
0.044
0.044
0.044
Inversion rate
0.1
0.1
0.1
0.1
IS transposition rate
0.1
0.1
0.1
0.1
RIS transposition rate
0.1
0.1
0.1
0.1
One-point recombination rate
0.3
0.3
0.3
0.3
Two-point recombination rate
0.3
0.3
0.3
0.3
Gene recombination rate
0.3
0.3
0.3
0.3
Gene transposition rate
0.1
0.1
0.1
0.1
Fitness function
Eq. (3.8)
Eq. (3.8)
Eq. (3.8)
Eq. (3.8)
Success rate
98%
94%
79%
69%
Exactly-one-on Functions
This series of
n
-exactly-one-on functions also begins with the identity func-
tion (or 1-exactly-one-on function) and the XOR (or 2-exactly-one-on func-
tion). But this is where the similarity ends: the 3-exactly-one-on function is
very different from the odd-3-parity function and if there is some pattern in
the design of this series of functions one must again start by studying the
structure of the 2-exactly-one-on function and all the other functions up in
the hierarchy while using functions of lower order as UDFs.
The exactly-one-on functions are very interesting and challenging for two
main reasons. The first one is that the sum-of-products solutions to these
functions are fairly compact already as the number of 1's in the output bits is
very small and grows very slowly according to the linear equation y =
n
,
where
y
is the number of 1's in the output bits and
n
corresponds to the order
