Cogging torque is a known disadvantage of surface permanent magnet (SPM) machines, especially if equipped with open stator slots. A possible strategy to reduce the cogging torque is to use suitably designed non-isotropic magnetic wedges. The design of such wedges for cogging torque minimization requires a genetic optimization approach. This has been done in previous works using Finite Element Analysis (FEA) simulations to predict the cogging torque for each machine design being explored, leading to a very time consuming optimization process. In this paper, the same optimization is performed using an analytical method to compute the cogging torque. It is shown that the optimization process, based on the analytical formula for cogging torque prediction, leads to the same result as the FEA-based procedure, but with a significant reduction in the computational burden.