Information Technology Reference
In-Depth Information
fore generalizes slightly better than the model (5.19) evolved by the GEA-B
algorithm. More formally, the model (5.20a) can be expressed by the follow-
ing C++ function:
double apsModel(double d[])
{
double dblTemp = 0.0;
dblTemp = (d[0]*((0.371673+d[0])+(0.371673*d[0])));
dblTemp += log((d[0]*d[0]));
dblTemp += sin(sin(sin(sin(sin(0.371673)))));
dblTemp += (d[0]*((d[0]+d[0])+d[0]));
dblTemp += (exp((exp(0.371673)+d[0]))/exp(sin(-0.977906)));
return dblTemp;
}
(5.20b)
where
d
0
corresponds to the independent variable
a
. Note how different this
model is from the model (5.19) designed without numerical constants. Here
the numerical constants play a prominent role as they were directly inte-
grated into the solution. Note, however, that the designed model is structur-
ally very different from the target function (5.15) despite being an extremely
accurate model as both the R-square and the plots of the target function and
the model show (Figure 5.14).
25
20
Target
15
Model
10
5
0
-1.2
-0.6
0.0
0.6
1.2
-5
-10
Figure 5.14.
Comparison of the target function (5.15) with the model (5.20) evolved
by the GEP-NC algorithm, that is, using a fixed set of five numerical constants. The
R-square was evaluated over the same testing set of 100 random points and is
equal to 0.999990385.
