Digital Signal Processing Reference
In-Depth Information
Fig. 3.6
Results of the
NSGA-II in Scenario II:
(
a
) optimal solutions and
(
b
) values of the objective
functions at the zeroth and
100th generations are
respectively represented by
circles
and
squares
a
(
1
)
whereas an effort to obtain the solution of only (
3.21
) would result in
|
|=
T
. This implies that Pareto-optimal solutions provide a set
of compromised solutions varying in between two extrema that are approximately
equal to the individual solutions of the objective functions when solved separately.
Similarly, for the Scenario II which had the strongest target-reflectivity along
the first subcarrier, we found that the MOO-solutions lied on an approximately
straight-line locus drawn on the surface of a sphere and varied from
[
0
.
0652
,
0
.
9975
,
0
.
0262
]
|
a
opt
|=
T
. Comparing with the individual so-
lutions of the objective functions in Scenario II, we noticed that (
3.21
) resulted
in
T
to
[
0
.
6339
,
0
.
6510
,
0
.
4182
]
|
a
opt
|=[
1
,
0
,
0
]
a
(
1
)
T
; whereas the solution of (
3.39
) still produced
|
|=[
0
.
9992
,
0
.
0374
,
0
.
0015
]
a
(
3
)
T
because it was a function of the system matrix
|
|=[
0
.
6261
,
0
.
6578
,
0
.
4187
]
only.
In addition, to assess the speed of convergence to these Pareto-optimal solutions,
in Figs.
3.5
and
3.7
we depict the relative change in values of the three objective
functions at different generation indices for both the target scenarios under con-
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