The process of applying generalized minimum aberration criteria (GMAC) to non-regular fractional factorial designs is extremely computationally intensive. Constructing and ranking all designs can take hours if not days; therefore, exploitation of the massively parallel nature of modern graphics processing units (GPUs) are used to perform the task. The computation is not just ported to the GPU, but is implemented as to optimize performance based upon the modern GPU architecture. Optimizations include using bit operations and table lookups to reduce the number of addition and multiplication operations performed. Tables are housed in GPU constant memory with almost no latency for access. Using a statistical proof from previous research reduces the memory required for the calculation. Optimizations regarding memory storage and transfer in NVIDIA's Compute Unified Device Architecture (CUDA) are also explored, as well as advance features such as streams and multiple GPUs. Experimental results have demonstrated the effectiveness of the proposed approach.