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Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence


Finding solutions to oddparity functions with ADFs 

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 subETs is much more flexible and no assumptions whatsoever are made concerning the structure of the evolved solutions.
Table 4.22
Parameters for the oddnparity problem using ADFs.

Odd2 
Odd3 
Odd4 
Odd5 
Odd6 
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 
Onepoint
recombination rate 
0.3 
0.3 
0.3 
0.3 
0.3 
Twopoint
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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