Permanent-magnet synchronous machines can be designed to obtain high efficiency and high torque density. Population-based optimization methods such as genetic algorithms and particle swarm optimization are gaining acceptance as a means of optimizing the design of this class of machines. This paper builds on the literature by utilizing a computationally efficient machine analysis appropriate for use with population-based optimization methods that enables the consideration of a significantly larger search space than previously reported in the literature. It is also unique in that the relative performance of different parameter encoding and objective function formulations are considered.