This paper discusses the multi-objective optimization of axial flux permanent magnet (AFPM) machines with ferrite spoke-type magnets, utilizing 3D finite element models. Three-dimensional finite element analysis is computationally expensive, and furthermore, substantial computation time is expended by optimization algorithms in evaluating low performing designs whose performance is far from the optimum if the search space is not specified correctly. In this regard, this work proposes two new methods for identifying the search space. The search is limited to ranges of input geometric variables where high performing designs are likely to be found. The optimization algorithm utilized is based on surrogate models and differential evolution. It is found that the combined use of these approaches drastically reduces the solution time.