The performance greatly benefits from the self-attention mechanism in Transformers, which could capture long-range dependencies Non-linear functions are prevalent in Transformers and their lightweight well, but with a substantial overhead in computation variants, incurring substantial and frequently underestimated and memory. Extensive research has been conducted to facilitate the hardware costs. Previous state-of-the-art works optimize deployment of Transformers on edge devices. Techniques like lightweight these operations by piece-wise linear approximation and store the structure integrating convolution and linear attention [4, 5] parameters in look-up tables (LUT), but most of them require unfriendly emerge, while quantization [6-8] and run-time pruning [9] has become high-precision arithmetics such as FP/INT 32 and lack consideration favored approaches to further reduced the hardware burden. of integer-only INT quantization. This paper proposed a However, the optimization of non-linear operations is frequently genetic LUT-Approximation algorithm namely GQA-LUT that can neglected in Transformer-based models which can be costly due to automatically determine the parameters with quantization awareness.