Using Adaptive Surrogate Models to Accelerate Multi-Objective Design Optimization of MEMS

Abstract

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. By addressing key limitations of traditional approaches, such as the consideration of objective constraints and the provision of multiple design options, the proposed framework enhances both flexibility and practical applicability. Results show that adaptive optimization outperforms traditional offline methods by delivering a greater number and higher quality of optimal solutions while requiring fewer finite element method simulations. The adaptive approach showed a significant advantage by attaining high-quality solutions while requiring only 2.8% of the finite element method (FEM) evaluations compared to traditional methods that do not incorporate surrogate models. This performance boost highlights the advantages of online learning in enhancing the accuracy, speed, and diversity of solutions in MEMS optimization. These optimization schemes were tested on multiple MEMS devices with varying physics and complexities, specifically the U-shaped Lorentz force actuator, serpentine Lorentz force actuator, and thermal actuator. The results highlight the robustness and versatility of the proposed methods, particularly in addressing cases involving discrete design variables and strict objective constraints. This comprehensive, step-by-step framework serves as a valuable resource for researchers and practitioners aiming to optimize MEMS designs from the ground up, providing a reliable and effective approach to multi-objective optimization in MEMS applications.

Keywords: Gaussian process regression; Lorentz force actuator; MEMS; design optimization; finite element method; multi-objective optimization; online learning; surrogate modeling; thermal actuator.

Figure 1

Flowchart of A-SAMOO integration with NSGA-II.

Figure 2

Schematic of the Lorentz force actuator.

Figure 3

MAPE of surrogate models for the U-shaped actuator with varying training sizes and preprocessing. (a) Shows the full plot; (b) highlights the low-MAPE region.

Figure 4

MAPE after optimization for the U-shaped Lorentz force actuator.

Figure 5

Number of true optimal solutions for the U-shaped Lorentz force actuator.

Figure 6

Hypervolume of predicted solutions for the U-shaped Lorentz force actuator.

Figure 7

Schematic of the serpentine Lorentz force actuator.

Figure 8

MAPE of surrogate models with different training sizes and preprocessing for the serpentine Lorentz force actuator. To improve readability, the y-axis is capped at 100%.

Figure 9

Actual vs. predicted plot for the serpentine Lorentz force actuator with a training size of 200.

Figure 10

MAPE after optimization for the serpentine Lorentz force actuator. To improve readability, the y-axis is capped at 100%.

Figure 11

Number of true optimal solutions for the serpentine Lorentz force actuator.

Figure 12

Hypervolume of predicted solutions for the serpentine Lorentz force actuator.

Figure 13

Schematic of the thermal actuator.

Figure 14

MAPE of surrogate models with different training sizes and preprocessing for the thermal actuator. To improve readability, the y-axis is capped at 100%.

Figure 15

Actual vs. predicted plot for the thermal actuator with a training size of 200.

Figure 16

MAPE after optimization for the thermal actuator. The y-axis is capped at 100% for clarity. (a) shows the complete plot, while (b) provides a zoomed-in view of the low-error region.

Figure 17

Number of true optimal solutions for the thermal actuator.

Figure 18

Hypervolume of predicted solutions for the thermal actuator.