Information Technology Reference
In-Depth Information
explicit constants are used as terminals; the second, called GEP-NC, uses a
fixed set of numerical constants and handles them explicitly either to create
new ones or to incorporate them directly in the evolving programs; the last
one, called GEP-RNC, uses the facility to manipulate directly random nu-
merical constants. The comparison between the three approaches will be
made on four different problems. The first is an artificial problem of se-
quence induction requiring integer constants; the second is a computer gen-
erated problem of function finding requiring floating-point constants; and
the last two are complex real-world problems from two different fields: di-
agnosis of breast cancer and analog circuit design.
5.6.1 Problems and Settings
For the sequence induction task, the following test sequence was chosen:
a
n
4
n
4
3
n
3
2
n
2
n
(5.14)
where
n
consists of the nonnegative integers. This sequence was chosen be-
cause it can be exactly solved by all the three algorithms and therefore can
provide an accurate measure of their performance in terms of success rate.
For this problem, the first 10 positive integers
n
and their corresponding
term were used as fitness cases (Table 5.5). The mean squared error, evalu-
ated by equation (3.4a), was used as basis for the fitness function, with the
fitness being evaluated by equation (3.5) and, therefore,
f
max
= 1000. This
experiment, with its three different approaches, is summarized in Table 5.6.
Table 5.5
Set of fitness cases for the sequence induction problem.
n
1
2
3
4
5
6
7
8
9
10
a
n
10
98
426
1252
2930
5910
10738
18056
28602
43210
For the function approximation problem, the following “V” shaped func-
tion was chosen:
y
= 4.251
a
2
+ ln(
a
2
) + 7.243
e
a
(5.15)
where
a
is the independent variable and
e
is the irrational number 2.71828183.
Evolutionary algorithms have some difficulties in solving exactly (that is,
