IEEE Computational Intelligence Magazine - August 2022 - 57

B. Control Policies
In this study, the term containment strategy
refers to a set of control policies. Each policy
influences one specific parameter, has a
trigger time 0$ and
# tn
, and is further
described by a Bézier curve (see Figure 2
for an example). The curve represents the
time in relation to strength of adjustment.
The adjustments are additive, meaning that
the value of each parameter at a given
time t is equal to its base value plus the
value of the policy for t. The curves are
defined via 16 control points. The height
(y-value) for each control point is 0$ and
# 1 and represents the relative policy
strength. The points #1 and #2 are always
fixed at (0, 0) and (10, 0), because it is
assumed that policies must start from zero
strength at the beginning of the pandemic.
While the next 14 points also have fixed
times, their heights are considered variable
and are subject to optimization in the
experiments to find optimal values for
them. The point #3 has time 15, and a
height always equal to the point #4, with
a time of 20. The idea is to group these
unusually close together to facilitate a
rapid response from zero strength to the
onset of the pandemic. All following
points are regularly spaced, with independent
height values. The last point has a
time of tn. The curve is still constructed
exactly as described above for policies
with a trigger time > 0. However, the
curve is subsequently scaled on the x-axis
so that the x-value of the first point coincides
with the trigger time, while the last
point remains at tn.
C. Optimization
Given the above model, the multi-objective
optimization problem can be defined
as follows. The decision space of the problem
is built by the parameters related to
the control policies. The policies have
fixed trigger times, and the first three control
points for each policy are predefined.
That leaves 13 control points per policy
for which the simulation experiments
need to find optimal y-values. All other
model parameters, including the number
and type of policies to be optimized, are
predefined and constant throughout the
optimization. The vector of decision variables
is denoted as d and the vector of all
other predefined parameters as m. Therefore,
each individual solution s is defined by
the individual vectors d and m. Applying
Loss of Immunity
Infection
S
E
Incubation
I
Death
Preventive
Quarantine
Suspected
Infection
Preventive
Quarantine
D
Diagnosis
Death
Sq
Eq
Incubation
Iq
Recovery
Rq
Preventive
Quarantine
Recovery
R
Loss of Immunity
Sq
Eq
I
Iq
D
Rq
Pandemic
Influence
GDP
FIGURE 1 The top graph shows the model compartments for the pandemic simulation. The bottom graph shows which of the pandemic
compartments are influencing the economy compartment.
AUGUST 2022 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 57

IEEE Computational Intelligence Magazine - August 2022

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