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.