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CMA-ES-based topology optimization accelerated by spectral level-set-boundary modeling
Computer Methods in Applied Mechanics and Engineering ( IF 6.9 ) Pub Date : 2024-08-27 , DOI: 10.1016/j.cma.2024.117331
Shin Tanaka , Garuda Fujii

Topology optimization commonly encounters several challenges, such as ill-posedness, grayscale issues, interdependencies among design variables, multimodality, and the curse of dimensionality. Furthermore, addressing the latter two concurrently presents considerable difficulty. In this study, we introduce a framework aimed at mitigating all the above obstacles simultaneously. The objective is to achieve optimal configurations in a notably reduced timeframe eliminating the need for the initial trial-and-error iterations. The topology optimization approach we propose is implemented via precise structural boundary modeling utilizing a body-fitted mesh generated using a Fourier series expanded level-set method. This methodology expedites the exploration of optimal solutions. We employ the covariance matrix adaptation-evolution strategy to address multimodality, thereby enhancing the optimization process. The implementation of the Fourier-series-expanded level-set method reduces the number of design variables while maintaining accuracy in finite-element analyses by replacing design variables from discretized level-set functions with the coefficients of the Fourier series expansion. To facilitate the exploration of optimal solutions, a method is also introduced for handling box constraints through an adaptive penalty function. To demonstrate the effectiveness of the proposed scheme, we address three distinct problems: mean compliance minimization, heat flux manipulation, and the control of electromagnetic wave scattering. Despite each system being governed by different equations, topology optimization method consistently yields notable acceleration in computational efficiency across all scenarios, and remarkably without requiring initial guesses.

中文翻译:


通过频谱水平集边界建模加速基于 CMA-ES 的拓扑优化



拓扑优化通常会遇到一些挑战,例如病态性、灰度问题、设计变量之间的相互依赖性、多模态和维度的诅咒。此外,同时解决后两者存在相当大的困难。在这项研究中,我们引入了一个旨在同时缓解上述所有障碍的框架。目标是在显著缩短的时间范围内实现最佳配置,无需进行初始试错迭代。我们提出的拓扑优化方法是通过精确的结构边界建模实现的,该建模利用使用傅里叶级数扩展水平集方法生成的体拟合网格。此方法加快了对最佳解决方案的探索。我们采用协方差矩阵适应进化策略来解决多模态问题,从而增强优化过程。傅里叶级数扩展水平集方法的实现通过将离散级集函数中的设计变量替换为傅里叶级数展开的系数,减少了设计变量的数量,同时保持了有限元分析的准确性。为了便于探索最优解,还引入了一种通过自适应惩罚函数处理箱约束的方法。为了证明所提出的方案的有效性,我们解决了三个不同的问题:均值柔度最小化、热通量操纵和电磁波散射的控制。尽管每个系统都由不同的方程控制,但拓扑优化方法在所有场景中始终能显著提高计算效率,并且无需初始猜测。
更新日期:2024-08-27
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