Multipoint design optimization of the shape of vane-type vortex generators (VGs) and their arrangement on swept wings are conducted using computational fluid dynamics in order to provide designs that are suitable for both cruise and critical conditions. The optimization is divided into two phases: the VG arrangement is optimized using the NASA Common Research Model (CRM) after the VG shape is optimized on a swept infinite wing with a cross-sectional airfoil of the CRM. The shape optimization reveals that VG height and incidence angle control the aerodynamic performance under cruise and critical conditions, and VGs with higher length-to-height ratios show better performance. One of the shape-optimized VGs has been used in this study to optimize the VG arrangement to ensure static stability of the pitching moment with minimally increased drag under cruise conditions. Optimized VG arrangements can prevent shock-induced separation from propagating to wing tips around the Yehudi break of the CRM wing. One optimal solution reduces conventional VG drag penalties by 50%.