This is the last part of a three-part paper regarding performance analysis and optimization of a centrifugal compressor used in a 100 kW microturbine. This part deals with the numerical constrained optimization of the diffuser apparatus (i.e. the radial and deswirl cascades) for maximum aerodynamic efficiency and pressure recovery. The optimization is accomplished through the application of a multiobjective Pareto evolutionary algorithm which is interfaced to a parametric code, that generates the geometries to be analyzed, and a Computational Fluid Dynamics code that measures the fitness of the candidate solutions. The variables of the optimization include the main dimensions of diffuser (with a constraint on the overall radial and axial size) and the profiles' shape. The set of optimized configurations is illustrated and compared to the original one; the reason of improved performance are finally discussed.