Growing interest and demand for efficient, cost-effective propulsion for small spacecraft platforms have driven the endeavor devoted to downscaling electric propulsion systems. Cusped field thrusters (CFTs) are advantageous over other electrostatic types such as gridded ion engines and Hall Effect thrusters, featuring enhanced electron confinement enabled by magnetic mirror using permanent magnets hence longer lifetime expectation. Physical modeling and characterization of performance are essential for design optimization of CFTs, but rather few research efforts have been dedicated to them to date. A multi-objective design optimization study is performed in the present study, based on evolutionary algorithms incorporating magnetic simulation coupled with an improved power balance model. It aims to simultaneously maximize the performance parameters, namely thrust, total efficiency, and specific impulse, with the anode voltage and current, mass flow rate, and magnet radii employed as the decision variables. Covariance-based global sensitivity analysis is conducted to identify influential design parameters. Uncertainty analysis is performed using prediction from surrogate models via machine learning by means of Monte Carlo simulation to examine the effects on uncertainties in the design parameters on the performance parameters. The plasma behavior inside the channel and the plume region has been investigated with primary focus on the magnetic field strength. In so doing, physical insights have been gained into key design factors to maximize CFT performance.