Information Technology Reference
In-Depth Information
⎨
r
i
,
j
x
(
High
)
j
+ 1
+
x
(
Low
)
j
x
(
Low
)
j
−
INT
x
(
ML
+1)
i
,
j
<
x
(
Low
)
j
INT
x
(
ML
+1)
i
,
j
>
x
(
High
)
j
x
(
ML
+1)
i
,
j
=
if
∨
⎩
(7.5)
x
(
ML
+1)
i
,
j
otherwise
where
,
i
= 1
,...,
n
pop
,
j
= 1
,...,
n
param
Discrete values can also be handled in a straight forward manner. Suppose that the
subset of discrete variables,
X(d)
, contains
i
elements that can be assigned to variable
x
:
X
(
d
)
=
x
(
d
)
i
x
(
d
)
i
<
x
(
d
)
i
+1
i
= 1
,...,
l
where
(7.6)
Instead of the discrete value
x
i
itself, its index,
i
, can be assigned to
x
.Nowthe
discrete variable can be handled as an integer variable that is boundary constrained to
range
{
1
,
2
,
3
,..,
N
}
. In order to evaluate the objective function, the discrete value,
x
i
,
is used instead of its index
i
. In other words, instead of optimizing the value of the
discrete variable directly, the value of its index
i
is optimized. Only during evaluation
is the indicated discrete value used. Once the discrete problem has been converted into
an integer one, the previously described methods for handling integer variables can be
applied. The principle of discrete parameter handling is depicted in Fig 7.2.
Fig. 7.2.
Discrete parameter handling
7.3.2
DSH Applications on Standard Evolutionary Algorithms
DSH has been used in many previous experiments in standard EAs as well as in ge-
netic programming like techniques. An example of the usage of DSH in mechanical
engineering problem in C++ language in given in Fig 7.3.
Here, only the set of discrete values is described in order to show that DSH is basi-
cally a field of values (real values) and individuals in integer form serve like pointers to
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