IEEE Computational Intelligence Magazine - August 2022 - 59

[7]. Realistic parameter fitting for the
current pandemic situation is nontrivial
and beyond the scope of this study. Having
equal starting conditions, the experiment
results differ only in their
containment strategies.
The optimization algorithms are run
for 10,000 evaluations with a population
size of 100. Only the population size for
MOEA/D had to be set
simulations start at t0 0=
to 91. The
and run until
tn = 300. The best performing algorithm
for each experiment setting is
determined by the hyper volume (HV)
[22] value and the individual distributions
of solutions against the objectives.
(1, 1, 1) represents the reference vector
for the HV calculations, since each
objective function has a normalized
value between 0 and 1. Each algorithm
is run 31 times. For each experiment
setting, an aggregated set of non-dominated
solutions is determined from the
results of each run to provide an indepth
evaluation. A correlation analysis
is used to identify the importance of
individual parameters.
A. Results
Table IV shows an aggregation of the
experiment results. f1
1 and f2
f 13
1 represent
simulations with the highest possible
parametric influence
^h ,= meaning
that the influence curve's height is
always 1. This demonstrates the potential
of isolated parameter adjustments.
Note that this doesn't necessarily correspond
to the best result for any of the
objectives. The following values represent
the median values, including the
corresponding standard deviation, for
the Pareto front with the highest hyper
volume HV out of all 31 trials. For each
trial, fmin
R
1
R
and fmin
2
represent the minimal
median value of f1 or f2 and HVR
represents the median HV. For f3, the
maximum value fmax
R
3
since the minimum value of f 03
^hlR
3
R
3
is of interest,
= is a
representation of solutions in Eno. The
last column fmax
from fmax
displays the values
multiplied by the number of
policies contained in the strategy. For
instance, the experiment setting ENPI
represents strategies with four policies,
hence
f3
TABLE I Combinations of parameter adjustments.
SYMBOL
sd.+ld.
NPI
PI
cr, pqr, cdp & pqer
dr, iqrr & vr
NPI + PI
NPI + PI + ECON
dr, iqrr, vr, cr, pqr, cdp & pqer
dr, iqrr, vr, cr, pqr, cdp, pqer,
(GDP)pi, (GDP)pqi & (GDP)peqi
Rlmax
= 4· max
3
f . This presents an
alternate view in which the assumed
cost of the employed strategy scales
with the number of parameter adjustments
used. Regarding the experiments
on this new model, there are three
trends to observe: first, even adjusting
single parameters can have major effects.
Optimizing cr, pqr, or cdp produces high
HV values, which can be an indicator
for the importance of NPIs in general.
Second, using non-NPI related policies
without simultaneously employing NPI
policies has a very limited effect. It is
observable that either the first infection
wave hits the population before effective
PIs are available or that the vaccine
TABLE III Model parameters.
PARAMETER
Extended SEIR Model Parameters
Initial S
Initial E
Initial I
Initial Sq, Eq, Iq, R, Rq, D
Contact Rate cr*
Transmission Probability tp
Incubation Rate ir
PARAMETER ADJUSTMENTS
cr & pqr
DECISION VARIABLES
26
52
39
91
130
Preventive Quarantine Rate
pqr*
Preventive Quarantine End
Rate pqer*
Contact Detection Probability
cdp*
Diagnosis Rate dr *
Infection Recovery Rate irr
Infection Quarantined
Recovery Rate iqrr*
TABLE II Boundaries for the adjustment of parameters (LB [lower boundary],
UB [upper boundary], TT [trigger time]).
POLICY/PARAMETER
Contact Rate
Preventive Quarantine Rate
Contact Detection Probability
Diagnosis Rate
Infected Quarantined Recovery Rate
Vaccination Rate
Preventive Quarantine End Rate
(GDP) Pandemic Influence
(GDP) Preventive Quarantine Impact
(GDP) Exposed Quarantined Impact
SYMBOL
cr
pqr
cdp
dr
iqrr
vr
pqer
(GDP)pi
(GDP)pqi
(GDP)peqi
LB
−7*
−0.03
−0.2
−0.2
* Negative, since cr enforces contact reduction between individuals in absolute values.
UB
0.5
0.6
2/14
1/42
1/100
1/14
TT
0.05
0.05
0.25
0.1
0.1
0.1
Immunity Loss Rate ilr
Vaccination Rate vr*
Death Probability dp
Economy Model Parameters
Initial GDP
Baseline Growth bg
Pandemic Influence pi*
Preventive Quarantined
Impact pqi*
Exposed Quarantined Impact
eqi*
Infected Impact ii
Infected Quarantined Impact
iqi
VALUE
0.98
0.01
0.01
10
0.05225
1/7
1/14
1/14
1/14
1/14
1/90
0.01
0.019346
0.12
0.4
0.4
0.6
0.8
* parameters that are considered for optimization
in the experiments
AUGUST 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 59
IEEE Computational Intelligence Magazine - August 2022

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - August 2022
