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Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence
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| Finding solutions to odd-parity functions with ADFs |
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Automatically defined functions were introduced in section
2.2.3. As you recall, in this complex system, normal genes encode a particular ADF whereas homeotic genes control which genes/ADFs are expressed in each cell. We also learned in
chapter 2 that the number of cells per organism (or, in other words, the number of homeotic genes per chromosome) is arbitrary and, as the fitness of the individual is determined by the fitness of the best cell, the greater the number of cells the higher the probability of evolving the right cell or solution. But there is one caveat though: we cannot go on increasing the number of cells indefinitely because it takes time and resources to express all of them. As shown in
Table 4.22, a total of three cells per individual is a good compromise.
As you can see in Table 4.22, the performance of this approach, in terms of success rate, is nearly the same as in the previous ones. But remember that the system is much more complex and requires the fine tuning of many more parameters. One advantage of this system, though, is that the linking of the sub-ETs is much more flexible and no assumptions whatsoever are made concerning the structure of the evolved solutions.
Table 4.22
Parameters for the odd-n-parity problem using ADFs.
| |
Odd-2 |
Odd-3 |
Odd-4 |
Odd-5 |
Odd-6 |
| Number
of runs |
100 |
100 |
100 |
100 |
100 |
| Number
of generations |
50 |
50 |
50 |
100 |
200 |
| Population
size |
30 |
10 |
30 |
30 |
30 |
| Number
of fitness cases |
4 |
8 |
16 |
32 |
64 |
| Function
set |
A O N |
A O N
X |
A O N
X |
A O N
X |
(A O N
X)2 |
| Terminal
set |
a b |
a b c |
a b c
d |
a b c
d e |
a b c
d e f |
| Number
of normal genes |
3 |
3 |
3 |
3 |
3 |
| Head
length of normal genes |
5 |
5 |
5 |
5 |
5 |
| Linking
functions |
A O N |
A O N
X |
A O N
X |
A O N
X |
A O N
X |
| Number
of homeotic genes |
3 |
3 |
3 |
3 |
3 |
| Head
length of homeotic genes |
3 |
5 |
5 |
5 |
5 |
| Chromosome
length |
54 |
66 |
66 |
66 |
66 |
| Mutation
rate normal genes |
0.044 |
0.044 |
0.044 |
0.044 |
0.044 |
| 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 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
| Gene
transposition rate |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
| IS
transposition rate |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
| IS
elements length |
1,2,3 |
1,2,3 |
1,2,3 |
1,2,3 |
1,2,3 |
| RIS
transposition rate |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
| RIS
elements length |
1,2,3 |
1,2,3 |
1,2,3 |
1,2,3 |
1,2,3 |
| Success
rate |
100% |
94% |
95% |
95% |
96% |
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