Development of an efficient global optimization method based on adaptive infilling for structure optimization

For problems with expensive black-box functions, the surrogate-based optimization (SBO) is more efficient than the conventional evolutionary algorithms in searching for the global optimum. However, the SBO converges much slower and shows imperfection in local exploitation, along with the increase of the scale of the design space, the number of the design variables, and the nonlinearity of the problems. This paper proposes an efficient global optimization method, which integrates an adaptive infilling by fuzzy clustering algorithm into an SBO process based on Kriging model. In each refinement cycle, a Kriging model is first built using samples in the current design space; then a fuzzy clustering algorithm is adopted to partition the design space into several subspaces considering inner features of the samples. Thus, new infilling samples are selected within each subspace by maximizing the expected improvement of the objective function and minimizing the surrogate prediction. Thereafter, the design space is updated by merging those subspaces, resulting in a diminishing design space during refinement. Furthermore, the parameters for the adaptive infilling procedure are studied to recommend reasonable settings for running optimizations. The proposed method is finally validated and assessed by eight analytical tests with bound constraints, and then employed in a beam optimization problem and a rocket interstage optimization problem under nonlinear constraints. The results indicate that the adaptive infilling behaves quite well in space exploration due to sampling in clustered subspaces, and possesses good performance in local exploitation as well because of space reduction.