<p>This study presents a comprehensive optimization and performance evaluation of three distinct inerter-based tuned mass damper (TMD) configurations (C3, C4, and C6) for seismic vibration control. The optimal parameters for three different structural damping ratios (0%, 2%, and 5%) and a wide range of mass ratio (0 to 0.1) suitable for practical applications are determined in the frequency domain using the Sequential Quadratic Programming (SQP) algorithm to minimize the displacement response. To bridge the gap between complex optimization and practical engineering, novel empirical design formulas are proposed, enabling researchers to determine optimal parameters for C3, C4, and C6 configurations without requiring exhaustive computational effort. Unlike previous studies, the study presents a rigorous validation of inerter effectiveness through an extensive suite of 160 ground motions, providing a granular comparison of performance under near-fault excitations versus far-fault records. Results demonstrate that while inerter-based systems significantly outperform classical TMDs in the frequency domain, their comparative superiority in the time domain is more bound, with average response reduction improvements of approximately 5%. The inerter-based TMDs exhibit the highest efficiency in mitigating kinetic energy, followed by displacement and acceleration. Notably, the effectiveness of the control systems is found to be highly sensitive to ground motion characteristics and structural damping, where higher damping ratios consistently lead to reduced control performance. Considering the trade-off between seismic efficiency and mechanical simplicity, the C6 configuration is identified as the most viable solution for structural protection.</p>