In this microfluidic application, microfluidic analysis of an active micro-mixer with an oscillating stirrer in a straight microchannel was performed. The effects of molecular diffusion and disturbance by the stirrer for mixing were examined. The mixing was simulated using the Lattice Boltzmann method incorporating a D2Q9 model. In this study, a time-averaged mixing index was used to estimate the mixing performance of a time-dependent flow. The results revealed that the mixer, using an oscillating stirrer, was much more enhanced and stabilized. In order to predict an effective mixing index, an optimum design for an active micro-mixer with an oscillating stirrer was performed based on successive Kriging method using optimal Latin hypercube sampling, and genetic algorithm. Parameters for the optimal design were determined to be the reduced frequency, and the length and the rotation angle of the stirrer. Optimal design parameters were determined to be 1.46, 0.8D and ${pm}55.8^{circ}$, respectively. These parameter values in the optimal design improved the mixing index of the initial design by up to 71.79%.