Surrogate-assisted topology optimization with hybrid Gabor and discrete cosine transform spectral parameterization

Despite the fact that topology optimization has become an efficient tool for addressing a wide range of structural and multiphysics design problems, the derivation of sensitivities remains extremely challenging for certain complex cases, while non-gradient optimization algorithms are often limited in handling high-dimensional topology representations. This study proposes a topology optimization method based on a reduced-dimensional spectral representation of the design domain constructed from two classes of basis functions. In the proposed topology representation model, the topology is encoded as a superposed spectral field, where discrete cosine transform (DCT) basis functions capture low-frequency global features and Gabor filters enhance detailed features. This hybrid representation enables a reduced-dimensional topology description with a small number of design variables. To tackle highly non-convex and non-smooth optimization problems, the covariance matrix adaptation evolution strategy (CMA-ES) algorithm performs global search through probabilistic sampling, with adaptive updates of the covariance matrix and step size to iteratively guide the search toward promising regions of the design space. Furthermore, a surrogate model incorporating a Gaussian process regression (GPR)-based pre-screening mechanism is established, enabling efficient elite sample selection prior to high-fidelity evaluation. Numerical examples examine the effects of the hybrid Gabor and Discrete Cosine Transform topology representation model on topology evolution and demonstrate that the proposed method can effectively address complex nonlinear and multiphysics optimization problems with reduced design dimensionality.