An industry-strength hybrid optimization approach, involving derivative-free global search followed by derivative-free local refinement, is proposed to solve the multi-dimensional problem of compact model parameter extraction and reduce its multi-objective nature while retaining the original device physical formulations. An intelligent transition method is employed to combine Differential Evolution and Nelder-Mead algorithms from a curated selection of machine learning-driven optimizer candidates, achieving better-fitting performance in various operating regions for the first time. Extraction results for compact models such as ASM-HEMT with 35 parameters and BSIM4 with 29 parameters in 3 steps show that a bestfit error of less than 0.2% is achieved with significantly less automatic extraction time of 1800 seconds compared to hours of global search alone and weeks of traditional manual parameter tuning. A new cost function is introduced to reduce sensitivity to outliers and introduce region appropriate automatic weights while preserving device physical formulations. This approach helps reduce total optimization time by a factor of 2-4 times compared to global optimization alone and reduces dependency on modeling know-how