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double apsModel(double d[])
{
double dblTemp = 0.0;
dblTemp = (exp(4)/((d[2]*d[2])+((77/pow(40,d[2]))+d[0])));
dblTemp += (((d[2]/37)*sqrt(d[2]))-d[0]);
dblTemp += (77-d[2]);
dblTemp += sqrt((4+((d[0]/log((((d[0]/4)-d[2])+40)))*d[2])));
dblTemp += (exp(4)/(pow(d[1],d[1])+(((37+37)/(4+40))+d[0])));
dblTemp += ((d[2]*sqrt(log(37)))/((sqrt(77)-d[1])-
(40-(37*d[0]))));
return dblTemp;
}
(5.27b)
It is worth pointing out how profusely the algorithm makes use of the five
available numerical constants: in fact, with the exception of one (constant
12), all of them were used to design this accurate model. Note also how
structurally different this program is from the model (5.26) designed without
numerical constants, especially in terms of the composition of the most abun-
dant function nodes.
The best solution created with the GEP-RNC algorithm was found in gen-
eration 4961 of run 30. Its genes and corresponding arrays of random nu-
merical constants are shown below (the sub-ETs are linked by addition):
Gene 1: /?+P?--ab??P??cacaaba??b?4027503030058
C
1
:
{11, 70, 24, 15, 83, 29, 82, 21, 16, 49}
Gene 2: QcQE*+??cPE*c?babbabac?b?1370963974448
C
2
:
{92, 28, 4, 5, 41, 35, 48, 99, 81, 33}
Gene 3: /?+?Pcbba/-?cccaccab???ca2719004069141
C
3
:
{81, 54, 73, 60, 44, 83, 3, 12, 68, 30}
Gene 4: +--/a?c?+-QEccababc??c?ac8512372841014
C
4
:
{40, 59, 8, 58, 94, 13, 71, 52, 23, 58}
Gene 5: /P?QQQcQ*a?a?c??ca??acbc?3064768815876
C
5
:
{40, 86, 33, 6, 83, 56, 7, 86, 59, 54}
Gene 6: ?--?bL/**a?Qbca?ca?caa?a?4314917061824
C
6
:
{92, 74, 34, 96, 56, 49, 34, 33, 58, 4} (5.28a)
This model has a fitness of 84.4035 and an R-square of 0.9655103219 evalu-
ated against the training set of 40 fitness cases and, therefore, is consider-
ably better than the model (5.26) designed without numerical constants and
