Cheap-expensive multi-objective Bayesian optimization for permanent magnet synchronous motor design

Bayesian optimization (BO) is a popular optimization technique for expensive-to-evaluate black-box functions. We propose a cheap-expensive multi-objective BO strategy for optimizing a permanent magnet synchronous motor (PMSM). The design of an electric motor is a complex, time-consuming process that contains various heterogeneous objectives and constraints; in particular, we have a mix of cheap and expensive objective and constraint functions. The expensive objectives and constraints are usually quantified by a time-consuming finite element method, while the cheap ones are available as closed-form equations. We propose a BO policy that can accommodate cheap-expensive objectives and constraints, using a hypervolume-based acquisition function that combines expensive function approximation from a surrogate with direct cheap evaluations. The proposed method is benchmarked on multiple test functions with promising results, reaching competitive solutions much faster than traditional BO methods. To address the aforementioned design challenges for PMSM, we apply our proposed method, which aims to maximize motor efficiency while minimizing torque ripple and active mass, and considers six other performance indicators as constraints.