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et al., 2011). In symbolic regression via GP, populations of equations
are genetically bred and through this process both the functional
form and numerical coeffi cients of the regression equation are
determined by an evolutionary mechanism. Elements in the
function set may include arithmetic operations (+, −, *, /, etc.),
mathematical functions (exp, log, cos, sin, tan, etc.), conditions
(If-Then-Else), and Boolean operations (AND, OR, and NOT). Two
types of GP algorithms were employed:
1.
standard GP
, where a single population is used with a restricted
or an extended function set; and
2.
multi-population (island model) GP
, where a fi nite number of
populations is adopted.
The amounts of four polymers, namely PEG4000, PVP K30, HPMC
K100, and HPMC E50LV, were selected as independent variables,
while the percentage of nimodipine released in 2 and 8 hours
(Y
2h
and Y
8h
) and the time at which 90% of the drug was dissolved,
were selected as responses.
Optimal models were selected by minimization of the Euclidean
distance between predicted and optimum release parameters.
Symbolic regression generated by a standard GP proposed the
following optimal regression equations:
Y
2h
= ((X
1
/X
3
)/exp(X
4
))/(exp(X
3
)−X
2
*X
3
)
[5.25]
Y
8h
= (exp(((X
3
∧
2)))
∧
(((X
1
*X
4
)
∧
exp(8.36))−((X
3
∧
X
1
)
∧
(X
1
*X
1
)))) [5.26]
t
90%
= (−0.06+X
3
)*((X
3
∧
X
1
)
∧
(X
2*
X
4
))
[5.27]
Symbolic regression via multi-population GP resulted in the
production of more complex equations, consisting of the basic
functions:
Y
2h
= X
1
/(X
1
−0.36*(−1.03*X
2
+X
3
)*(−3.87*(0.17/X
2
+X
3
)
−(0.18/X
2
+X
3
+2.7*(−0.11+2.86*(X
1
−X
4
)))*(X
1
−X
4
))+X
4
+0.8*(−0.47+2*X
3
+(−0.1−X
3
)*(X
1
+0.26/X
2
−X
3
+(X
1
∧
2)
*(X
1
−X
4
))−0.29*X
2
*X
4
))
[5.28]
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