Digital Signal Processing Reference
In-Depth Information
f
(
v
1
)=
g
(
x
1
) = 285
f
(
v
2
)=
g
(
x
2
)=
−
273
f
(
v
3
)=
g
(
x
3
)=
−
288
f
(
v
4
)=
g
(
x
4
)=
−
285
f
(
v
5
)=
g
(
x
5
)=
−
33
.
Next, we apply mutation and randomly suppose chromosome 3 and bit 6
are chosen. Thus, the mutated chromosome is 010101 and gives a further
improvement of
f
to -288.
Simulation parameters
To determine the solution of the given optimization problem, we will
choose the following parameters: the population consists of 100 distinct
chromosomes, and we choose 5950 random pairs for selection.
Simulation results
The results achieved after one cycle, including the above-mentioned
operators, are the following:
f
(
v
1
)=
g
(
x
1
) = 285
f
(
v
2
)=
g
(
x
2
)=
−
289
f
(
v
3
)=
g
(
x
3
)=
−
288
f
(
v
4
)=
g
(
x
4
)=
−
285
f
(
v
5
)=
g
(
x
5
)=
−
33
.
Thebestvalueis
x
min
= 21. We can show that the GA converges toward
the minimum of the given function. The fact that this solution is reached
is more a coincidence than a property of the GA. It's important to
emphasize that a GA may not find an exact optimal solution, but most
often finds solutions close to the neighborhood of the global optimum.
As a final remark, it's very important to mention that GAs can be
very well applied in combinatorial optimization where the decision vari-
Search WWH ::
Custom Search