A surrogate-assisted algorithm based on principal component analysis and partial least squares regression space projection strategies for high-dimensional expensive problems

This paper proposes a surrogate-assisted evolutionary algorithm (SAEA) for expensive, high-dimensional problems, named RDDSP-SAEA (Reduced-Dimension Decision Space Partition−SAEA). The proposed algorithm is based on the DSP-SAEA framework and expands on the original method by incorporating a Multi-Decision Space Partitioning (MDSP) approach for global search and an Enhanced Surrogate Pool (ESP) for local search. In the local search, the ESP strategy integrates Principal Component Analysis (PCA) and Partial Least Squares (PLS) regression techniques to generate more reliable surrogates in lower-dimensional spaces. In the MDSP global search, the original decision space and additional lower-dimensional projections are partitioned and clustered. Radial Basis Function (RBF) surrogates are trained on the various regions within these decision spaces, and only the projection that yields the best models is selected for further global exploration. The algorithm is evaluated on test problems ranging from 30 to 1000 variables and compared against classical and recent competitive algorithms, as well as on a real-world engineering problem. The main contribution of this study is the proposal of an improved DSP-SAEA algorithm for optimizing expensive problems, which outperforms other state-of-the-art SAEAs, particularly for test cases with 300, 500, and 1000 variables.