This paper proposes an Adaptive Grey Wolf Optimizer based on Transfer function Inertia Weight of Second-order High-pass Filter (SAGWO), aiming to overcome the limitations of Grey Wolf Optimizer (GWO) in terms of convergence speed and solution accuracy. SAGWO enhances the algorithm's dynamic adaptability and greatly speeds up convergence by incorporating the transfer function of the second-order high-pass filter into the modifications of inertia and leader wolves' weight. Furthermore, SAGWO incorporates an adaptive random search component, which significantly enhances the search range and the ability to explore globally. The performance of SAGWO is assessed and compared against three prominent Swarm Intelligence Algorithms (ALO, WOA, and EHO), along with GWO and GWO optimized by PSO. This evaluation is conducted through trials on the CEC2017 standard test set. The experimental results indicate that SAGWO outperforms in terms of both convergence speed and solution correctness. Moreover, SAGWO is utilized to address practical engineering problems such as pressure vessel design and robot gripper design, showcasing its remarkable effectiveness once more. This research enhances the theoretical development of Swarm Intelligence Algorithms and demonstrates the significant utility of SAGWO in practical applications, establishing it as a powerful instrument for scientific investigation and engineering optimization.