|
For the sequence induction problem, the first 10 positive integers
an and their corresponding term N were used as fitness cases. The fitness function was based on the relative error with a selection range of 20% and maximum precision (0% error), giving maximum fitness
fmax = 200 (Ferreira
2001).
For the “V” shaped function problem, a set of 20 random fitness cases chosen from the interval [-1, 1] was used. The fitness function used was also based on the relative error but in this case a selection range of 100% was used, giving
fmax = 2000.
For the time series prediction problem, using an embedding dimension of 10 and a delay time of one, the sunspots series presented in
Table 1 result in 90 fitness cases. In this case, a wider selection range of 1000% was chosen, giving
fmax = 90,000.
In all the experiments, the selection was made by roulette-wheel sampling coupled with simple elitism and the performance was evaluated over 100 independent runs. The six experiments are summarized in
Table 2.
Table 2
General settings used in the sequence induction (SI), the “V” function, and sunspots (SS) problems. The “*” indicates the explicit use of random constants.
| |
SI* |
SI |
V* |
V |
SS* |
SS |
| Number
of runs |
100 |
100 |
100 |
100 |
100 |
100 |
| Number
of generations |
100 |
100 |
5000 |
5000 |
5000 |
5000 |
| Population
size |
100 |
100 |
100 |
100 |
100 |
100 |
| Number
of fitness cases |
10 |
10 |
20 |
20 |
90 |
90 |
| Function
set |
+
- * / |
+
- * / |
+
- * / L E K ~ S C |
+
- * / L E K ~ S C |
4
(+ - * /) |
4
(+ - * /) |
| Terminal
set |
a, ? |
a |
a, ? |
a |
a -
j, ? |
a - j |
| Random
constants array length |
10 |
-- |
10 |
-- |
10 |
-- |
| Random
constants range |
{0,
1, 2, 3} |
-- |
[-1,1] |
-- |
[-1,1] |
-- |
| Head
length |
6 |
6 |
6 |
6 |
8 |
8 |
| Number
of genes |
7 |
7 |
5 |
5 |
3 |
3 |
| Linking
function |
+ |
+ |
+ |
+ |
+ |
+ |
| Chromosome
length |
140 |
91 |
100 |
65 |
78 |
51 |
| Mutation
rate |
0.044 |
0.044 |
0.044 |
0.044 |
0.044 |
0.044 |
| One-point
recombination rate |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
| Two-point
recombination rate |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
0.3 |
| Gene
recombination rate |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
| IS
transposition rate |
0.1 |
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 |
1,2,3 |
| RIS
transposition rate |
0.1 |
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 |
1,2,3 |
| Gene
transposition rate |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
| Random
constants mutation rate |
0.01 |
-- |
0.01 |
-- |
0.01 |
-- |
| Dc
specific transposition rate |
0.1 |
-- |
0.1 |
-- |
0.1 |
-- |
| Dc
specific IS elements length |
1,2,3 |
-- |
1,2,3 |
-- |
1,2,3 |
-- |
| Selection
range |
20% |
20% |
100% |
100% |
1000% |
1000% |
| Precision |
0% |
0% |
0% |
0% |
0% |
0% |
| Average
best-of-run fitness |
179.827 |
197.232 |
1914.8 |
1931.84 |
86215.27 |
89033.29 |
| Average
best-of-run R-square |
0.977612 |
0.999345 |
0.957255 |
0.995340 |
0.713365 |
0.811863 |
| Success
rate |
16% |
81% |
-- |
-- |
-- |
-- |
|