A dynamic Gaussian process surrogate model-assisted particle swarm optimisation algorithm for expensive structural optimisation problems

Abstract

The computational analysis of real-world engineering structures is typically evaluated using time-consuming simulation calculations, which means that it is difficult to balance computational burden and precision when applying traditional algorithms to large-scale complex structures. To solve this expensive structural optimisation problems, a new optimisation algorithm (CPSO-GPR) is proposed, based on particle swarm optimisation with a constriction factor (CPSO) and a dynamic Gaussian process regression (GPR) surrogate model. In the CPSO-GPR, the CPSO is used as a global optimisation framework, and the GPR is trained to accelerate local searches. The acceleration strategy consists of two parts. First, a local high-accuracy GPR is dynamically provided to approximate complex real fitness around the current best particles. Second, based on the explicit GPR output, the best particles are rapidly predicted using Newton’s method. Moreover, the GPR is retrained at each iteration of Newton's method by a continual updating of training sample datasets. Using the above strategy, the number of function evaluations is significantly reduced. To validate the proposed CPSO-GPR, it was compared to several existing algorithms on eight benchmark functions and two engineering cases. The results demonstrate that the CPSO-GPR has clear advantages in terms of higher efficiency and higher precision than the existing algorithms, and it offers promising performance in computationally expensive engineering optimisation problems.