This paper presents the minimum column-to-beam moment ratio of steel moment resisting frame (SMRF) with various connection models using the non-dominated sorting genetic algorithm-II (NSGA-II). We evaluate the minimum column-to-beam moment ratio of SMRF required to ensure the beam-sway mechanism by the pushover analysis. We investigate the influence of the connections on the minimum column-to-beam moment ratio. We consider WUF-W and RBS as the connection models. The optimal algorithm used in this paper is to minimize the structural weight and the column-to-beam moment ratios through the objective functions and to induce the beam-hinge mechanism through the constraint which is to prevent the formation of plastic hinge at the column part consisting of joints. Using the 3-story example, we compare the minimum column-to-beam moment ratio of SMRF required to ensure the beam-sway mechanism according to the connection models.