CMA-ES-based structural topology optimization using a level set boundary expression—Application to optical and carpet cloaks

Abstract

In this paper, we propose a topology optimization method based on the covariance matrix adaptation evolution strategy (CMA-ES) as a method for solving multimodal structural optimization problems. CMA-ES optimizes level set functions as design variables to minimize the fitness value that is regularized to avoid the ill-posedness of topology optimization using a perimeter constraint. Explicit boundaries between the material and void are obtained using the iso-surface of linearly interpolated level set functions. To show the effectiveness of the proposed method for multimodal structural optimization problems, topology optimization for optical and carpet cloaks is numerically demonstrated. The proposed computational strategy is robust to the settings of the initial configurations, even if the topology optimization problems have multimodal distributions of solutions that include many local minima with insufficient performance, and stably improves the regularized fitness value. The obtained optimal configurations have good performance, and we can obtain them without the trial and error of seeking appropriate initial configurations and adapting strategy parameters.