The utility of scale factor adaptation in differential evolution

Micro differential evolution (mDE) refers to algorithms that evolve with a small population to search for good solutions. Although mDEs are very useful for resource-constrained optimization tasks, the research on mDEs is still limited. In this paper, we propose a new mDE, i.e., vectorized bimodal distribution based mDE (called VB-mDE). The main idea is to employ a vectorized bimodal distribution parameter adjustment mechanism in mDE for performance enhancement. Specifically, in the VB-mDE, two important control parameters, i.e., scale factor F and crossover rate C⁢R, are adjusted by bimodal Cauchy distribution. At the same time, to increase the population diversity, the scale factor F is vectorized. The proposed VB-mDE is evaluated on the CEC2014 benchmark functions and compared with the state-of-the-art mDEs and normal DEs. The results show that the proposed VB-mDE has advantages in terms of solution accuracy and convergence speed.

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Structural Design and Optimization of a Resonant Micro-Accelerometer Based on Electrostatic Stiffness by an Improved Differential Evolution Algorithm

Micromachines ◽

10.3390/mi13010038 ◽

2021 ◽

Vol 13 (1) ◽

pp. 38

Author(s):

Libin Huang ◽

Qike Li ◽

Yan Qin ◽

Xukai Ding ◽

Meimei Zhang ◽

...

Keyword(s):

Resonant Frequency ◽

Differential Evolution ◽

Structural Design ◽

Proof Mass ◽

Differential Evolution Algorithm ◽

Scale Factor ◽

Global Optimality ◽

Evolution Algorithm ◽

Improved Differential Evolution Algorithm ◽

Micro Accelerometer

This study designed an in-plane resonant micro-accelerometer based on electrostatic stiffness. The accelerometer adopts a one-piece proof mass structure; two double-folded beam resonators are symmetrically distributed inside the proof mass, and only one displacement is introduced under the action of acceleration, which reduces the influence of processing errors on the performance of the accelerometer. The two resonators form a differential structure that can diminish the impact of common-mode errors. This accelerometer realizes the separation of the introduction of electrostatic stiffness and the detection of resonant frequency, which is conducive to the decoupling of accelerometer signals. An improved differential evolution algorithm was developed to optimize the scale factor of the accelerometer. Through the final elimination principle, excellent individuals are preserved, and the most suitable parameters are allocated to the surviving individuals to stimulate the offspring to find the globally optimal ability. The algorithm not only maintains the global optimality but also reduces the computational complexity of the algorithm and deterministically realizes the optimization of the accelerometer scale factor. The electrostatic stiffness resonant micro-accelerometer was fabricated by deep dry silicon-on-glass (DDSOG) technology. The unloaded resonant frequency of the accelerometer resonant beam was between 24 and 26 kHz, and the scale factor of the packaged accelerometer was between 54 and 59 Hz/g. The average error between the optimization result and the actual scale factor was 7.03%. The experimental results verified the rationality of the structural design.

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