IEEE Computational Intelligence Magazine - August 2022 - 64

It is evident that getting close to optimal f1 or f2 values
is possible with little cost, ... However, the less costly
a containment strategy is, the stronger is its inherent
trade-off.
further evaluations-this study uses a
significance level of
p ..1005
The tests show that all experiment
settings differ significantly from each
other according to their HV after the
elimination of inconsequential strategies.
Although most experiment settings
result in differing f1 values, several
of the tested combinations are very
similar in this respect. Looking at f2, it
is of interest that E ..sd
NPI
lar to (. ).
ENPIPI+
E p 04996
=
is highly similar to (p =
0.1507). The comparison regarding f3
is not necessary because it is only a
secondary objective in this model,
guiding the algorithms to converge to
efficient containment strategies. The
next examination tests if the trials with
the best HV value differ significantly
from the other algorithms' trials for
each experiment setting. Using HV to
compare the groups, in Ecr
MOEA/D
is indifferent from GLMONSGA III(.
)
(. ). Testing the f1 values, all
p 0 1432=
p 0 2847=
algorithms differ significantly from
the algorithm with the best HVR
value. Testing f2 and f3, the same
insights apply in most cases, but some
tests fail when comparing NSGA - II
and
(. ), Ep 01594
sd..ld+ = 0 1078
p 0 1871=
p
E
=
p
GLMONSGA II- . As such, ENPI
pqr (. ), and
E (. ) do not differ from
each other for these two algorithms
according to their f2 values. In case
of (. )
p 0 0660=
NPIPI+ = 00925 and ENPI+ECON
(. ) the values of f3 show no
significant difference.
F. Discussion
This work's approach to finding optimal
control strategies during pandemics
highlights dynamics inherent to the
HED and is suited to support decisionmaking.
However, the presented simulation
results do not directly translate to
and from GLMONSGA II+ld
is highly simiLikewise,
the
current pandemic situation. The
model parameters must be continuously
calibrated to ensure a good fit
for a specific pandemic situation for a
real-world application. Additionally,
parameter limits for the containment
measures need to be estimated realistically.
The suggested containment
strategies need to be interpreted
regarding a possible real-world implementation,
which raises questions
such as what it means to employ a
policy at a specific strength.
In this work, the chosen model
parameters and boundaries for the optimization
experiments have the purpose
to demonstrate this novel approach, to
identify general correlations within the
model, and to see where parallels and
general insights can be found towards
real-world scenarios. The length of the
simulated pandemic is limited to a specific
timeframe. It should be kept in mind
that this can bias the results to favor solutions
optimized for the chosen timeframe.
In Figure 6(a) for example, it
seems that the end of two of the three
employed policies coincides perfectly
with the end of the simulated timeframe.
This reduces the cost objective of the
strategy without the consequences of
abruptly terminating such measures. As
the pathogen requires time to build up to
another wave, this wave never manifests
due to the cut-off point at the end of the
simulation. The results show that NPIs
tend to dominate over PIs. During the
simulation, it is possible to continuously
suppress the virus via NPIs, without ever
achieving herd immunity and without
having to deal with the long-term consequences
of that. Measures like the vaccine
with long-lasting effects could be more
cost-effective over longer timeframes.
That said, there is another reason why
NPIs might be favored by the optimization:
most NPIs influence a significantly
64 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2022
greater portion of the population, namely
the healthy population, than PIs, which
mostly target the much smaller fraction
of already infected individuals. Hence,
NPIs have a leverage advantage due to
the higher number of individuals with
which they can effectively work. Future
studies on integrated strategies with PIs
and NPIs can improve upon the presented
approach by considering longer timeframes
or indicators for herd immunity as
a termination criterion.
V. Conclusion
This paper explores novel pandemic
containment strategies regarding three
conflicting objectives. Implementing
multi-objective optimization allows the
identification of proper containment
strategies, producing minimal infection
peaks and minimal economic damage,
while having low overall cost in terms
of regulatory influence. The experiments
are based on an extended version of the
SEIR compartmental model, with an
integrated economic compartment and
a model for dynamic containment strategies.
The results indicate that there are
significant trade-offs between the three
objectives to be optimized simultaneously.
At least one objective has to be
sacrificed, since maintaining both a stable
economy and health-care system
relies on significant intervention efforts.
In addition, the results suggest that
employing economic or pharmaceutical
measures without NPIs has limited
effects. NPIs have proven to be the most
effective and important measures in
containing the simulated pandemic.
Future works should integrate the
parameter estimation ex ante, to validate
the model using real-world data. The
presented approach can also be extended
by working on a dynamic time-horizon
for the simulation duration, or by integrating
a more comprehensive representation
of the economy and its
corresponding objective. In conclusion,
the multi-objective optimization
approach has high potential for detecting
optimal and novel containment
strategies, although it remains challenging
to interpret the results for real-world
decision-making.
IEEE Computational Intelligence Magazine - August 2022

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