Parametric study and multipoint design optimization of vortex generator (VG) arrangements on a swept infinite-wing are performed by using computational fluid dynamics (CFD) to explore a desirable VG design under both cruise and critical condition. We examine the effects of VG height, length, incidence angle, and spacing on lift-drag ratio at a low angle of attack, which determines aerodynamic performance under cruise condition, and stall characteristics shown as lift curves representing critical condition. The present simulation model considers a single VG equipped on a super-critical rectangular wing and the periodic boundary condition is adopted in the span direction to reduce the cost of CFD analysis. Computational results show that the spacing affects mainly on the lift-drag ratio at a low angle of attack but has no effect on values of lift coefficients at a high angle of attack. The spacing determines the angle of attack at which buffet begins. In contrast, the height controls the shape of lift curves and maximum lift coefficients while it has much smaller effect on lift-drag ratio at a low angle of attack than the spacing. Both optimization and parametric study results show that the VG height and incidence angle control the balance of aerodynamic performances under cruise and critical condition while VGs with higher length to height ratio achieve better performances than conventional VGs.