This study explores the optimization of bandgap characteristics in locally resonant metastructures through advanced artificial intelligence (AI) and optimization algorithms, focusing on the accurate estimation of resonator damping ratios. By developing a novel mathematical framework for metastructure analysis, this research diverges from traditional methods, offering a more nuanced approach to bandgap manipulation. This research significantly improves metastructure modeling accuracy by precisely estimating resonator and structural damping ratios, enhancing model fidelity crucial for analysis, control strategies, and design optimization. Through a combination of model simulations and experimental validation, the efficacy of the Hybrid Genetic Algorithm-Particle Swarm Optimization (GA-PSO) algorithm is demonstrated, highlighting its potential for practical applications in engineering metastructures. This paper not only provides a robust method for estimating damping ratios but also opens new avenues for future research, including the application of machine learning techniques and the development of intelligent materials. The findings of this study contribute to the foundational understanding necessary for the advancement of mathematical modeling metamaterials, with broad implications for industries where precise vibration control is crucial.