<p>The nonlinear energy sink (NES) has become a prominent technology in the field of vibration control, especially with the increasing performance requirements for equipment in precision instruments and structural safety. However, conventional NESs face limitations in robustness, with their efficiency being highly sensitive to vibration amplitudes. To address this, a novel NES with inerter and grounded nonlinear stiffness (ING-NES) is proposed to optimize vibration control efficiency. This study aims to conduct comprehensive research on the ING-NES to significantly enhance its vibration control capabilities and establish a new paradigm for advanced NES design. The research focuses on an ING-NES system, analyzing its performance through a combination of the incremental harmonic balance method and the Runge–Kutta method to determine system responses. The stability of the frequency response is evaluated using Floquet theory, ensuring the reliability of the analytical solutions. Computational results are compared with analytical solutions to validate the accuracy of the methods used. The study further investigates the parametric effects on the system’s performance and employs the grey wolf algorithm (GWO) for parameter optimization. A comparative analysis of vibration suppression efficiency between the ING-NES and the cubic NES is also conducted. The results demonstrate a strong correlation between analytical and numerical solutions, validating the effectiveness of the methods applied. The parameter optimization using GWO shows significant improvements in the vibration control efficiency of the ING-NES. Moreover, the study explores the global behavior of the ING-NES under varying excitation amplitudes and frequencies, revealing complex and chaotic motion responses. These findings indicate that the ING-NES design offers a promising direction for the development of advanced NES technologies, potentially leading to more effective vibration suppression solutions in various applications.</p>