Parameterized level set method accelerates CMA-ES based topology optimization for acoustic-elastic coupled systems

Topology optimization often faces some difficult properties such as grayscale, checkerboard pattern, high ratios of material parameters, multimodality, and the curse of dimensionality when applied to the design of acoustic metadevices. In particular, it is difficult to simultaneously overcome the multimodality and curse of dimensionality. Gradient-based algorithms using sensitivity for searching solution improve the objective function based on the gradient from a specific initial solution, thus, suffer from multimodal property and burdensome initial guesses are required. On the other hand, evolutionary algorithms struggle with the curse of dimensionality, and finding optimal configurations with high performance in high-dimensional design spaces is difficult. In topology optimizations, the spatial discretization of design variables and that of finite element analysis often share the same mesh, and reducing the design variables makes numerical analyses inaccurate due to the coarse finite element discretization. Here, we show an approach to simultaneously solve the above difficult properties, emerging frequently in the designs of acoustic metadevices, by introducing parameterization scheme for structural modeling in topology optimization to overcome the curse of dimensionality. To search for the optimal solution, we use CMA-ES, which has the best solution search performance among evolutionary algorithms, and overcome difficult properties such as multimodal property.