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Collocation method with flood-based metaheuristic optimizer for optimal control ...
Advantages of the Collocation Method: applications such as the multi-strain
COVID-19 model.
1- Efficient Transformation of OCP to NLP:
The collocation method turns the OCP Thus, the hybrid strategy combines the best
with infinite dimensions into an NLP with aspects of both approaches and creates a strong
finite dimensions. This makes it easier to and valuable framework for solving OCPs accu-
solve computationally. rately and reliably.
2- Accuracy and Stability: Laguerre polyno- Here, we organize the rest of the paper:
mials and their derivative operational ma- First, definitions and notes are presented, fol-
trices are used in the collocation method lowed by developing an optimal control strategy
to keep the numbers stable while getting for a multi-strain COVID-19 model in Section 2.
good state and control variable estimates. Section 3 outlines two methods for addressing this
3- Simplicity and Applicability: The issue. The results of computer experiments are
method’s straightforward implementation discussed in Section 4. Finally, Section 5 summa-
makes it suitable for handling complex rizes alternative research avenues in this field.
dynamical systems with nonlinear con-
straints. 2. Mathematical model for the
multi-strain co-infection
Advantages of the Flood-Based Meta-
heuristic Optimizer (FBMO): In this section, we develop a compartmental epi-
demic model to investigate a multi-strain COVID-
1- Global Optimization: FBMO is an algo-
19 scenario on disease propagation dynamics and
rithm based on nature that finds near- control measures. The OCP for the multi-strain
global optima in big, complicated opti- COVID-19 model is shown mathematically using
mization problems. It does this by get- the parameters and variables depicted in Tables 2
ting around the problems that local search and 3.
methods have.
Then, the multi-strain epidemic model can be
2- Computational Efficiency: The optimizer mathematically described as a nonlinear system
uses tools like erosion coefficients and of differential equations:
Gaussian random distributions to find the
best balance between exploration and ex-
dS βSI c
ploitation. This lets it quickly find high- =Λ − ψS − µS − βSI v − , (1)
dt 1 + αI c
quality solutions.
3- Robustness for Complex Systems: The dV = − βI v V − µV + ψS, (2)
FBMO is excellent at dealing with non- dt
linear constraints and big problems, as dI c
= − (µ + c c + ρw c + (1 − ρ)w c )I c
shown by its performance in benchmark dt
studies and engineering applications. βSI c
+ , (3)
1 + αI c
Improvements Achieved by the Hybrid
dI v
Strategy: =βI v V + βSI v + (1 − ρ)w c I c
dt
1- Enhanced Computational Efficiency: The − (µ + c v + wv)I v , (4)
hybrid strategy cuts computation time by dR
a large amount while keeping the quality dt = − µR + w v I v + ρw c I c , (5)
of the solution. It does this by combining
the structured approach of the colloca-
tion method with the global optimization based on the starting circumstances, where the
power of FBMO. values of S(0), E(0), I(0), V (0), and R(0) are not
negative. In addition, vaccines are effectual on
2- Improved Solution Quality: The hybrid the common strain but ineffectual on the ampli-
method makes sure that the estimates of fied strain, which is important for controlling the
the state and control variables are accu- propagation of multi-strain disease. We present
rate and reliable, and it solves the result- the flowchart of the model (1)-(5) as in Figure 1.
ing NLP quickly to find the best solutions. In our study, we introduce three key con-
trol strategies. Let u 1 (t) symbolize the adjust-
3- Scalability: The hybrid strategy is scal- ments to vaccination tactics. We utilize revised
able and adaptable to various complex disease transmission rates to illustrate the im-
OCPs, making it suitable for real-world pacts of isolation strategies and media coverage,
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