  Bayesian Optimization algorithm has become a promising approach for nonlinear
global optimization problems and many machine learning applications. Over the
past few years, improvements and enhancements have been brought forward and
they have shown some promising results in solving the complex dynamic problems,
systems of ordinary differential equations where the objective functions are
computationally expensive to evaluate. Besides, the straightforward
implementation of the Bayesian Optimization algorithm performs well merely for
optimization problems with 10-20 dimensions. The study presented in this paper
proposes a new high dimensional Bayesian Optimization algorithm combining
Recurrent neural networks, which is expected to predict the optimal solution
for the global optimization problems with high dimensional or time series
decision models. The proposed RNN-BO algorithm can solve the optimal control
problems in the lower dimension space and then learn from the historical data
using the recurrent neural network to learn the historical optimal solution
data and predict the optimal control strategy for any new initial system value
setting. In addition, accurately and quickly providing the optimal control
strategy is essential to effectively and efficiently control the epidemic
spread while minimizing the associated financial costs. Therefore, to verify
the effectiveness of the proposed algorithm, computational experiments are
carried out on a deterministic SEIR epidemic model and a stochastic SIS optimal
control model. Finally, we also discuss the impacts of different numbers of the
RNN layers and training epochs on the trade-off between solution quality and
related computational efforts.
