<p>Increasing reliance on inverter-based renewable energy sources has significantly reduced power grid inertia, posing critical challenges to frequency stability in modern power grids. Virtual Synchronous Generators (VSGs) have emerged as a promising solution by emulating the inertial and damping characteristics of conventional synchronous machines. However, the performance of VSGs depends heavily on the optimal tuning of key control parameters, such as virtual inertia and damping coefficients. This paper proposes an adaptive hybrid optimization algorithm, termed Quantum-Inspired Jellyfish Search Optimizer (QI-JSO), which integrates the exploration capability of the Jellyfish Search Optimizer with the Quantum-Inspired Evolutionary Algorithm (QIEA). This method employs an adaptive probability control strategy to dynamically balance exploration and exploitation, ensuring robust convergence. An Integrated Time and Absolute Error (ITAE)-based objective function has been used to simultaneously minimize frequency deviations and voltage deviations under disturbances. Simulation studies on a microgrid model demonstrate that QI-JSO-VSG achieves nearly 67% reduction in frequency deviation compared with conventional VSG, and nearly 55% frequency deviation reduction compared with QIEA-VSG. Also, the proposed method has been found to be 33% and 16% faster settling time than the conventional VSG and QIEA-VSG approaches, respectively. The proposed algorithm has been validated on 16 standard benchmark functions, achieving statistically significant superiority, and consistently outperforms other conventional algorithms in terms of convergence speed, accuracy, and stability. Results carried out from the simulation studies highlight QI-JSO as an effective and adaptive optimization framework for enhancing the resilience of VSG-based systems in renewable-integrated networks.</p>