This paper proposes a robust optimization algorithm customized for the optimal design of electric machines. The proposed algorithm, termed “robust explorative particle swarm optimization” (RePSO), is a hybrid algorithm that affords high accuracy and a high search speed when determining robust optimal solutions. To ensure the robustness of the determined optimal solution, RePSO employs the rate of change of the cost function. When this rate is high, the cost function appears as a steep curve, indicating low robustness; in contrast, when the rate is low, the cost function takes the form of a gradual curve, indicating high robustness. For verification, the performance of the proposed algorithm was compared with those of the conventional methods of robust particle swarm optimization and explorative particle swarm optimization with a Gaussian basis test function. The target performance of the traction motor for the optimal design was derived using a simulation of vehicle driving performance. Based on the simulation results, the target performance of the traction motor requires a maximum torque and power of 294 Nm and 88 kW, respectively. The base model, an 8-pole 72-slot permanent magnet synchronous machine, was designed considering the target performance. Accordingly, an optimal design was realized using the proposed algorithm. The cost function for this optimal design was selected such that the torque ripple, total harmonic distortion of back-electromotive force, and cogging torque were minimized. Finally, experiments were performed on the manufactured optimal model. The robustness and effectiveness of the proposed algorithm were validated by comparing the analytical and experimental results.