Permanentmagnet synchronous motors have been preferred in industrial fields for a few decades. It is reason for that the permanent magnet synchronous motors have high torque/volume ratio, large flux weakening region, and especially highly efficient. The main factor to obtain these advantages is the selection of suitable geometric parameters in their design optimizations. As a design optimizationthis study investigates external rotor permanent magnet synchronous motor with fractional slot windings. Pre-analytical designs and subsequently design optimizations by genetic algorithm and differential evolution algorithm have been studied. Thebetter resultsobtained were tested by the finite element method.Thus, so much more compact and efficient motor model was to be achieved based on the design geometries. The results are very reasonable and useful