Data-driven topology design with persistent homology for enhancing population diversity

Abstract

This paper proposes a selection strategy for enhancing population diversity in data-driven topology design (DDTD), a topology optimization framework based on evolutionary algorithms (EAs) using a deep generative model. While population diversity is essential for global search with EAs, conventional selection operators that preserve diverse solutions based on objective values may still lead to a loss of population diversity in topology optimization problems due to the high dimensionality of design variable space and strong nonlinearity of evaluation functions. Motivated by the idea that topology is what characterizes the inherent diversity among material distributions, we employ a topological data analysis method called persistent homology. As a specific operation, a Wasserstein distance sorting between persistence diagrams is introduced into a selection algorithm to maintain the intrinsic population diversity. We apply the proposed selection operation incorporated into DDTD to a stress-based topology optimization problem as a numerical example. The results confirm that topology can be analyzed using persistent homology and that the proposed selection operation significantly enhances the search performance of DDTD.

Figures (14)

• Figure 1: Schematic illustration of the proposed selection strategy
• Figure 2: Optimization flowchart of DDTD
• Figure 3: Schematic illustration of VAE
• Figure 4: Schematic illustration of selection operation in NSGA-II: (a) non-dominated sorting; (b) crowding distance sorting; (c) overall procedure
• Figure 5: Relationship between design variable space and objective space in multi-objective optimization problems with significant nonlinearity: (a) Solutions with similar design variables for different objective values; (b) Solutions with different design variables for similar objective values