Micro-electromechanical systems (MEMS) sensors and actuators are widely used in a variety of applications, from medical imaging to space telecommunications, making their optimal design crucial. Designing MEMS is a time-consuming process that requires numerous iterations of resource-intensive simulations to evaluate potential designs. As the number of design variables and objectives grows, the complexity and required computational time for this process also increase significantly. Consequently, most efforts to tackle this challenge have focused on scenarios with limited design parameters and a single objective, leaving the area of efficient multi-objective optimization (MOO) for MEMS devices relatively unexplored. In this study, we employ surrogate-assisted design optimization for a MEMS Lorentz force actuator. During an iterative multi-objective optimization process, surrogate models are utilized for performance evaluation of designs instead of numerical simulations. This approach enables us to achieve optimal designs that satisfy all objective constraints using as low as 2% of the number of simulations required compared to case surrogate models are not used, greatly facilitating design optimization. Additionally, we investigate how the number of training simulations and their preprocessing impact the accuracy of the surrogate models and the optimization results.