  This paper presents an Improved Bayesian Optimization (IBO) algorithm to
solve complex high-dimensional epidemic models' optimal control solution.
Evaluating the total objective function value for disease control models with
hundreds of thousands of control time periods is a high computational cost. In
this paper, we improve the conventional Bayesian Optimization (BO) approach
from two parts. The existing BO methods optimize the minimizer step for once
time during each acquisition function update process. To find a better solution
for each acquisition function update, we do more local minimization steps to
tune the algorithm. When the model is high dimensions, and the objective
function is complicated, only some update iterations of the acquisition
function may not find the global optimal solution. The IBO algorithm adds a
series of Adam-based steps at the final stage of the algorithm to increase the
solution's accuracy. Comparative simulation experiments using different kernel
functions and acquisition functions have shown that the Improved Bayesian
Optimization algorithm is effective and suitable for handing large-scale and
complex epidemic models under study. The IBO algorithm is then compared with
four other global optimization algorithms on three well-known synthetic test
functions. The effectiveness and robustness of the IBO algorithm are also
demonstrated through some simulation experiments to compare with the Particle
Swarm Optimization algorithm and Random Search algorithm. With its reliable
convergence behaviors and straightforward implementation, the IBO algorithm has
a great potential to solve other complex optimal control problems with high
dimensionality.
