This research introduces a novel methodology for optimizing Bayesian Neural Networks (BNNs) by synergistically integrating them with traditional machine learning algorithms such as Random Forests (RF), Gradient Boosting (GB), and Support Vector Machines (SVM). Feature integration solidifies these results by emphasizing the second-order conditions for optimality, including stationarity and positive definiteness of the Hessian matrix. Conversely, hyperparameter tuning indicates a subdued impact in improving Expected Improvement (EI), represented by EI(x). Overall, the ensemble method stands out as a robust, algorithmically optimized approach.