Digital Signal Processing Reference
In-Depth Information
b
0
>
)
2
=(
5
i=0
2
i
)
10
=
x
(
<b
5
···
b
i
·
Initial population
The initial population is randomly generated. Each chromosome repre-
sents a six-bit binary vector.
Evaluation function
The evaluation function
f
of the binary vector
v
is equivalent to the
function
g
(
x
):
f
(
v
)=
g
(
x
)
.
The five given
x
-values
x
1
= 37,
x
2
= 13,
x
3
= 35,
x
4
= 44, and
x
5
=6
correspond to the following five chromosomes:
v
1
= (100110)
,
v
2
= (001101)
,
v
3
= (100011)
,
v
4
= (101110)
,
v
5
= (000110)
The evaluation function provides the following values:
f
(
v
1
)=
g
(
x
1
)=0
f
(
v
2
)=
g
(
x
2
)=
−
225
93
f
(
v
4
)=
g
(
x
4
) = 336
f
(
v
4
)=
g
(
x
5
)=
f
(
v
3
)=
g
(
x
3
)=
−
−
64
.
We immediately see that
v
2
is the fittest chromosome since its
evaluation function provides the minimal value.
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