An improved optimization method combining particle swarm optimization and dimension reduction kriging surrogate model for high-dimensional optimization problems

Abstract

An improved optimization method is proposed which combines the particle swarm optimization (PSO) algorithm with the dimension reduction kriging surrogate model (DK), namely PSO + DK. In this method, a surrogate model is dynamically constructed and updated between the lower dimensional principal components and the response, instead of between the high-dimensional design variables and the response as in traditional methods. The key point of DK is that the principal components analysis (PCA) is integrated with the active learning kriging surrogate model (AK). Since PCA can reduce the dimension effectively, DK makes surrogate model construction possible for complex high-dimensional optimization problems. Numerical examples and four classical engineering problems are presented to validate the effectiveness of the proposed method. The results show that the proposed method can decrease the computational cost significantly while guaranteeing the precision compared with PSO and PSO + AK for high-dimensional optimization problems.

KEYWORDS:

• Kriging surrogate model; dimension reduction; principal components analysis; particle swarm optimization

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

Some of the models and data that support the study are available from the corresponding author upon reasonable request.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 52275266, 11832013 and 11572134], Hubei Provincial Department of Education Science and Technology Research Project [grant number Q20221714] and the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment [grant numbers DTL2023019 and DTL2022012].