This work presents the optimization of a dual circular-polarized (CP) shaped-beam reflectarray with improved performance. To that end, the design methodology leverages surrogate models based on support vector regression (SVR) of the electromagnetic response of the constituent unit cell for a direct layout optimization of the antenna. The dual CP capability is achieved using a linear polarization (LP) Jerusalem cross integrated with an LP-to-CP polarization converter. A full description of the reflectarray analysis in CP is given. We also provide a missing demonstration in the literature of the fact that the direct coefficients in CP shape the copolar (CO) pattern of the corresponding polarization. This is applied to the optimization of a dual CP reflectarray with an isoflux pattern, achieving a reduction of more than 9 dB in the crosspolar (XP) pattern.