This study presents a comprehensive multi-objective optimization framework specifically designed for micro-electromechanical systems (MEMS). The framework integrates both traditional and adaptive optimization techniques, named Surrogate-Assisted Multi-Objective Optimization (SAMOO) and Adaptive-SAMOO (A-SAMOO), respectively. These optimization schemes were tested on multiple MEMS devices with varying physics and complexities, demonstrating their robustness and versatility, particularly in handling cases with discrete design variables and strict objective constraints. Additionally, the study addresses several shortcomings of traditional approaches such as considering objective constraints and providing multiple design options for users, which enhances the flexibility and practical application of the results. The importance of preprocessing objectives is also emphasized. Results show that adaptive optimization outperforms traditional offline methods, delivering a greater number and higher quality of optimal solutions. This performance boost highlights the advantages of online learning in enhancing the accuracy, speed, and diversity of solutions in MEMS optimization. This detailed, step-by-step framework serves as a valuable guide for researchers and practitioners looking to optimize MEMS designs from scratch, offering a more reliable and effective approach to multi-objective optimization in MEMS applications.