パーシステントホモロジーによる位相的多様性評価を組み込んだデータ駆動型進化的トポロジー最適化

抄録

Topology optimization often requires solving multimodal and highly nonlinear opitimization problems with a huge number of design variables to achieve structural design with high degrees of freedom using complex physical models. However, conventional evolutionary algorithms, which are effective for multimodal and nonlinear optimization problem, cannot solve such high-dimensional problems. This study proposes a data-driven evolutionary topology optimization framework to overcome this challenge with dimensionality reduction. The proposed framework is based on data-driven multifidelity design and latent crossover, where design candidates generated by low-fidelity optimization are iteratively updated through high-fidelity evaluation and crossover in a low-dimensional latent space. We introduce a novel selection operation to address the issue that the diversity of solution distributions in the objective space and the design variable space does not align for multimodal multiobjective optimization problems. We utilize persistent homology to extract topological characteristics of structures, such as the number of connected components, voids, and their sizes, into persistent diagrams. By quantifying the differences between structures using the Wasserstein distance between corresponding persistent diagrams, we can quantitatively evaluate the topological differences among the structures. Combined with the conventional approach of ensuring diversity in the objective space, it provides a selection method that also preserves diversity in the design variable space. We apply the proposed method to a 2D structural design problem, and the results demonstrate that the selection based on persistent homology improves the search performance of the framework. Furthermore, the optimized structures outperform the performance of those obtained by conventional gradient-based optimization.