The rotor design of Synchronous Reluctance machines is considered in this paper, based on a multi-objective, genetic optimization algorithm and finite element analysis. Three different types of barrier geometries are compared, all described by a limited set of input variables. The aim of the paper is to investigate the relationships between the obtainable performance and the different barrier types. The two questions underlying this analysis are: which is the geometry that can potentially give the machine with the highest torque to volume ratio? Which is the geometry with the best compromise between number of input parameters (i.e. computational time) and performance? The results of the analysis show that Synchronous Reluctance machines can be designed using artificial intelligence in a reasonable time, obtaining adequate performances and rotor geometries consistent with the literature.