This work deals with the design optimization of electrical machines under the consideration of manufacturing uncertainties. In order to efficiently quantify the uncertainty, blackbox machine learning methods are employed. A multi-objective optimization problem is formulated, maximizing simultaneously the reliability, i.e., the yield, and further performance objectives, e.g., the costs. A permanent magnet synchronous machine is modeled and simulated in commercial finite element simulation software. Four approaches for solving the multi-objective optimization problem are described and numerically compared, namely: epsilon-constraint scalarization, weighted sum scalarization, a multi-start weighted sum approach and a genetic algorithm.