Frequency-domain thermoreflectance (FDTR) is a widely used technique for characterizing thermal properties of multilayer thin films. However, extracting multiple parameters from FDTR measurements presents a nonlinear inverse problem due to its high dimensionality and multimodal, non-convex solution space. This study evaluates four popular global optimization algorithms: Genetic Algorithm (GA), Quantum Genetic Algorithm (QGA), Particle Swarm Optimization (PSO), and Fireworks Algorithm (FWA), for extracting parameters from FDTR measurements of a GaN/Si heterostructure. However, none achieve reliable convergence within 60 seconds. To improve convergence speed and accuracy, we propose an AI-driven hybrid optimization framework that combines each global algorithm with a Quasi-Newton local refinement method, resulting in four hybrid variants: HGA, HQGA, HPSO, and HFWA. Among these, HPSO outperforms all other methods, with 80% of trials reaching the target fitness value within 60 seconds, showing greater robustness and a lower risk of premature convergence. In contrast, only 30% of HGA and HQGA trials and 20% of HFWA trials achieve this threshold. We then evaluate the worst-case performance across 100 independent trials for each algorithm when the time is extended to 1000 seconds. Only HPSO, PSO, and HGA consistently reach the target accuracy, with HPSO converging five times faster than the others. HPSO provides a general-purpose solution for inverse problems in thermal metrology and can be readily extended to other model-fitting techniques.