There is a clear demand for advanced electric propulsion systems for current and future satellite applications for a variety of commercial and research missions to reduce launch costs. The HEMP-T/CFT propulsion systems are very complex and require a detailed analysis of how design criteria influence performance. By downscaling the CFT, further propellant and system reductions would result in lower costs while maintaining high performance. The CFT concept has demonstrated significantly improved performance over the HET and GIT, however little is understood about the complexities of the interactions and interdependencies of the geometrical, magnetic and ion beam properties of the thruster. This study applies an advanced design methodology combining a modified power distribution calculation and evolutionary algorithms assisted by surrogate modeling to a multi-objective optimization for the performance optimization and characterization of the CFT. Optimization is performed for maximization of performance defined by 5 design parameters (i.e., Φa, Ia, ma, and magnet radii), simultaneously aiming to maximize 3 objectives, that is, thrust, efficiency and specific impulse. Statistical methods based on global sensitivity analysis are employed to assess the optimization results in conjunction with surrogate models to identify key design factors with respect to the 3 design objectives and additional performance measures. Significant effects of the anode power and magnet radii have been observed on the considered design criteria with the anode current exhibiting the most significant degree of influence on all 3 objectives. Several optimum design points were analyzed and one has demonstrated the most comprehensive advantages in important design criteria.