Surrogate-assisted multiobjective evolutionary algorithms (SAMOEAs) are a promising approach for solving expensive multiobjective optimization problems (EMOPs), wherein the number of function evaluations is extremely restricted due to expensive-to-evaluate objective functions. However, most SAEAs are not well-scaled to high-dimensional problems because the accuracy of surrogate models degrades as the problem dimension increases. This paper proposes a dimensionality reduction-based SAEA, which involves the following two strategies to address high-dimensional EMOPs. First, mapping high-dimensional training samples to a low dimensional space in building surrogate models can boost the accuracy of surrogate models. Second, compared to approximation-based surrogate models, reliable classification-based models can be obtained under a few training samples. Accordingly, the proposed algorithm is designed to integrate a dimensionality reduction technique into an existing classification-based SAEA, MCEA/D. It builds classification models in low-dimensional spaces and then utilizes these models to estimate good solutions without expensive function evaluations. Experimental results statistically confirm that the proposed algorithm derives state of-the-art performance in many experimental cases.

Surrogate-assisted evolutionary algorithms (SAEAs) are a promising approach for solving expensive multiobjective optimization problems, but they often cannot address high-dimensional problems. Although one common approach to this challenge is to construct reliable surrogates, their accuracy inevitably deteriorates in a high-dimensional search space. Thus, this paper presents a novel SAEA based on scalarization function approximation, which is designed to strengthen its robustness against this deterioration. The proposed algorithm constructs an approximation model for each scalarization function defined in a decomposition-based framework. Each decomposed problem is then solved using multiple independent models trained for its neighbor problems. The intent is to decrease the risk of search performance degradations caused by unreliable approximations and retain the redundancy of the surrogate-assisted search to hedge the risk of over-fitting. Furthermore, each approximation model is adapted to a promising region of its corresponding decomposed problem to reduce the complexity of model fitting given a limited number of training samples. Experimental results show that the proposed algorithm is competitive with state-of-the-art SAEAs adapted for high-dimensional problems.

Surrogate-assisted multi-objective evolutionary algorithms have advanced the field of computationally expensive optimization, but their progress is often restricted to low-dimensional problems. This manuscript presents a multiple classifiers-assisted evolutionary algorithm based on decomposition, which is adapted for high-dimensional expensive problems in terms of the following two insights. Compared to approximation-based surrogates, the accuracy of classification-based surrogates is robust for few high-dimensional training samples. Further, multiple local classifiers can hedge the risk of over-fitting issues. Accordingly, the proposed algorithm builds multiple classifiers with support vector machines on a decomposition-based multi-objective algorithm, wherein each local classifier is trained for a corresponding scalarization function. Experimental results statistically confirm that the proposed algorithm is competitive to the state-of-the-art algorithms and computationally efficient as well.