Data-Driven Multifidelity Topology Design With a Latent Crossover Operation

Abstract

Abstract Topology optimization is one of the most flexible structural optimization methodologies. However, in exchange for its high degree of design freedom, typical topology optimization cannot avoid multimodality, where multiple local optima exist. This study focuses on developing a gradient-free topology optimization framework to avoid being trapped in bad local optima. Its core is a data-driven multifidelity topology design (MFTD) method, in which design candidates generated by solving low-fidelity topology optimization problems are updated based on evolutionary algorithms (EAs) through high-fidelity evaluation. The key component of the data-driven MFTD is a deep generative model that compresses the dimension of the original data into a low-dimensional manifold, i.e., the latent space. In the original framework, convergence variability and premature convergence problems arise as the generative process is performed randomly in the latent space. Inspired by a popular crossover operation, we propose a data-driven MFTD framework incorporating a new crossover operation called latent crossover. We apply the proposed method to a maximum stress minimization problem in 2D structural mechanics. The results demonstrate that the latent crossover improves convergence stability compared to the original method. Furthermore, the optimized designs exhibit performance comparable to or better than that in conventional gradient-based topology optimization using the P-norm measure.