Information Technology Reference
In-Depth Information
As its expression shows, the program encoded in this structure matches per-
fectly the target sequence (5.14) (the contribution of each gene is shown in
brackets):
(5.18b)
a
n
(
n
3
3
n
2
)
(
0
)
(
n
2
)
(
4
n
4
4
n
3
)
(
n
)
4
n
4
3
n
3
2
n
2
n
Note how profusely the algorithm uses the random numerical constants at its
disposal, either by integrating them directly into the solutions or by combin-
ing them to create new ones.
It is worth pointing out that the GEP-RNC algorithm performs consider-
ably better than the GEP-NC algorithm at this task (a success rate of 75% as
opposed to 35%), showing that the facility invented for handling random
numerical constants in gene expression programming is not only elegant but
also extremely efficient. Indeed, thanks to its flexibility and efficiency, this
framework can be used to create more complex algorithms that require the
swift handling of vast quantities of random numerical constants, such as
algorithms for complete neural network induction, algorithms for polyno-
mial induction, parameter optimization, and decision tree induction.
5.6.3 “V” Function
To solve the “V” shaped function problem, a more varied function set con-
sisting of F = {+, -, *, /, Q, L, E, S, C} (“Q” represents the square root
function, “L” represents the natural logarithm, “E” represents
e
x
, “S” repre-
sents the sine function, and “C” represents the cosine) was chosen in order to
enrich the solution space and, therefore, provide more varied forms of repre-
senting numerical constants if need be. As usual, this function set was used
by all the three algorithms. For the GEA-B algorithm, the set of terminals
consists obviously of the independent variable
a
, thus giving T = {a}. For the
GEP-NC algorithm, besides the independent variable, five different rational
constants randomly chosen from the interval [-2, 2] and represented by the
numerals 1-5 were used, thus giving T = {a, 1, 2, 3, 4, 5}, where “1” repre-
sents the numerical constant -0.977906, “2” represents -0.505524, “3” repre-
sents 0.205841, “4” represents 1.6409, and “5” represents 0.371673. For the
GEP-RNC algorithm, the set of terminals consists obviously of T = {a, ?}
and the set of random numerical constants consisted again of 10 constants
represented by the numeral 0-9, thus giving R = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
The ephemeral random constant “?” ranged over the rational interval [-2, 2]
(see the complete list of all the parameters used per run in Table 5.8).
