Tuned Mass Dampers (TMDs) are widely used to mitigate structural vibrations in buildings and bridges. However, conventional optimization methods often struggle to achieve optimal performance due to the complexity of structural dynamics. This study proposes the NN-L-BFGS-B algorithm, which combines Artificial Neural Networks (ANNs) for global exploration and L-BFGS-B for local exploitation to efficiently optimize TMD parameters. A ten-story shear-building model with a TMD is used for validation. The proposed method achieves the lowest H₂ norm compared to previous studies, demonstrating improved optimization performance. Additionally, NN-L-BFGS-B effectively balances computational efficiency and accuracy, making it adaptable to various engineering optimization problems.