An Auto-Tuned Surrogate-Assisted Algorithm Based on Principal Component Analysis (PCA) and Partial Least Squares (PLS) Regression Space Projection Strategies for High-Dimensional Expensive Problems

Abstract

This paper introduces a surrogate-assisted evolutionary algorithm (SAEA) for high-dimensional single-objective continuous optimization problems with computationally expensive fitness evaluations. Named $\mu $ RDDSP ( $\mu $ Reduced-Dimension Decision Space Partitioning), the method builds on the DSP-SAEA framework and enhances it with an auto-tuned Multi-Decision Space Partitioning (autoMDSP) strategy for global search and an Enhanced Surrogate Pool (ESP) for local search. The autoMDSP partitions both the original decision space and lower-dimensional projections using a self-tuning clustering procedure. The most promising global samples are then refined by a global prescreening phase before the local search. In the local phase, a pool of surrogate models is built sequentially, aiming to continuously refine and optimize the global best solution. A simplified and faster version named RDDSP-SAEA is also presented as a variant to expand flexibility and increase the user’s options. Both algorithms are evaluated on benchmark problems with 100 to 1,000 decision variables and are also applied to a real-world engineering optimization problem. The proposed methods achieve better results compared to SAEAs such as DSP-SAEA, ESPSO, ESAO, SAMSO, GL-SADE, MLSAO, and CSRSA, particularly for problems with 300, 500, and 1,000 variables. Across all comparisons performed, the proposed methods achieved superior pairwise performance on 78% of the test instances, statistically similar performance on 5% of the test instances, and inferior performance in the remaining cases.