Surrogate-Assisted CMA-ES for Problems with Low Effective Dimensionality
Yuta Sekino, Yohei Watanabe, Kento Uchida, Shinichi Shirakawa · Proceedings of the Genetic and Evolutionary Computation Conference · 2025
High-dimensional optimization problems in real-world applications often possess the property called low effective dimensionality (LED), where only a small part of directions in search space affect the evaluation value, and others are redundant. On problems with LED, because the redundant directions deteriorate the prediction performance of the surrogate model, the performance of several surrogate-assisted evolutionary algorithms is worsened. This paper focuses on the doubly trained surrogate CMA-ES (DTS-CMA-ES) that employs Gaussian process regression as a surrogate model and proposes DTS-CMA-ES-LED by incorporating several countermeasures for LED to DTS-CMA-ES. The proposed method considers directions along the eigenvectors of the covariance matrix and evaluates the effectiveness of each direction using the estimated element-wise signal-to-noise ratio of the update directions. Then, the proposed method reconstructs the kernel function with the computed effectiveness to reduce the effect of redundant directions. We also introduce the hyperparameter adaptation mechanism and refinement of the step-size adaptation as countermeasures for LED. The experimental results show that DTS-CMA-ES-LED effectively optimized the benchmark functions with LED.