IEEE Computational Intelligence Magazine - August 2022 - 60

comes later into play than all other
measures. Third, containment strategies
consisting of multiple policies generate
the solutions with the highest HV values.
Even policies which had little or no
effect on their own can contribute in
these scenarios. While the estimated,
cost according to f3, is not necessarily
higher for these strategies, fmax
Rl
3
shows that this quickly changes when
the objective value is modified to
account for the number of parameter
adjustments. Therefore, it can be said
that the advantages of these strategies
would likely come with significantly
greater cost.
The footnotes of Table IV highlight
the best algorithm per experiment
regarding the HVR values. With few
exceptions, GLMONSGA IIperformed
the
best. Further evaluations concentrate
on the containment strategies with multiple
policies because they produce the
highest HV values. In-depth analysis of
these strategies allows assessing the
dynamics between the optimized parameters
and their influence on specific
objectives. Figure 3 shows the HV conTABLE
IV The containment strategies and corresponding performance indicators.
Table footnotes show the best algorithm according to the HV values.
EXPERIMENT
Eno
NPIs
Ecr
b
f1
1
0.4975
0.1960
Epqr
Ecdp
d
0.0765
d
0.1440
Epqer
PIs
Edr
c
-
0.4975
0.4371
Eiqrr
Evr
ECON
b
0.4882
b
0.4975
E()
E()
E()
COMBINATIONS
b
GDPpi
0.4975
-
GDPpqi
0.4975
-
GDPpeqi
Esd.ld.+
Esd.ld.+
l
ENPI
d
d
0.4975
0.0649
[7]*
-
0.0627
ENPI ECON+
ENPI PI+
d
d
0.0627
0.0627
ENPI PI ECON++
a NSGA - II.
b MOEA/D.
c GLMO with NSGA - III.
d GLMO with NSGA - II.
- No optimization.
* Reference experiment based on [7].
d
0.0627
f2
1
−3.0301
−4.9158
6.3634
0.9980
−3.0301
−3.8430
−3.3365
−3.5046
−3.5543
−3.0301
−3.0301
6.3466
-
5.0642
−0.8341
5.0555
−0.8428
RHV
-
0.5135 ±
0.0312
0.6238 ±
0.0011
0.5653 ±
0.0007
0.0000 ±
0.0000
0.1462 ±
0.0035
0.0225 ±
0.0000
0.0000 ±
0.0000
0.0000 ±
0.0000
0.0000 ±
0.0000
0.0000 ±
0.0000
0.7863 ±
0.0056
0.4201 ±
0.0000
0.8519 ±
0.0059
0.8828 ±
0.0085
0.9141 ±
0.0039
0.9261 ±
0.0058
R
f1
min
-
0.1088 ±
0.0051
0.0599 ±
0.0000
0.1115 ±
0.0001
0.4975 ±
0.0000
0.4025 ±
0.0001
0.4836 ±
0.0000
0.4975 ±
0.0000
0.4975 ±
0.0000
0.4975 ±
0.0000
0.4975 ±
0.0000
0.0509 ±
0.0001
0.1765 ±
0.0000
0.0496 ±
0.0004
0.0497 ±
0.0003
0.0496 ±
0.0001
0.0497 ±
0.0002
R
fmin
2
-
−4.9669 ±
0.0368
−3.0301 ±
0.0000
−3.0301 ±
0.0000
−3.0301 ±
0.0000
−3.8099 ±
0.0142
−3.2825 ±
0.0151
−3.4528 ±
0.0178
−3.5041 ±
0.0322
−3.0301 ±
0.0000
−3.0301 ±
0.0000
−4.9526 ±
0.0579
−3.4299 ±
0.0000
−4.9498 ±
0.0359
−4.9930 ±
0.0539
−5.4874 ±
0.0254
−5.4958 ±
0.0314
R
f3
max
-
0.8835 ±
0.0156
0.3095 ±
0.0312
0.8171 ±
0.0715
0.0000 ±
0.0000
0.8860 ±
0.0193
0.6205 ±
0.0622
0.6887 ±
0.0396
0.7454 ±
0.0753
0.0000 ±
0.0000
0.0000 ±
0.0000
0.4629 ±
0.0197
0.2545 ±
0.0000
0.5642 ±
0.0433
0.5223 ±
0.0637
0.4857 ±
0.0492
0.4859 ±
0.0548
0.9258
0.5090
2.2568
3.6561
3.3999
4.8590
Rlmax
f3
vergence of all four algorithms, which
are used in the simulation experiments.
While NSGA - II, GLMONSGA IIGLMONSGA
III,
and
perform equally well,
MOEA/D fails to converge to similarly
high HV values. However, it performs
reasonably when optimizing parameter
adjustments that influence only two of
three objectives, e.g.,
E .iqrr
Using Figure
4, it can be observed that MOEA/D
gets stuck locally, since the solutions
are dense around specific objective
values. The same figure shows, that
there is barely a difference between
60 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2022
IEEE Computational Intelligence Magazine - August 2022

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