Efficient adaptive surrogate-based optimization using fuzzy clustering for complex system optimizations

Adaptive infilling is a key element for Surrogate-based optimization (SBO) in its efficiency and convergence. For complex system optimization problems with expensive black-box functions, the SBO with common adaptive infilling shows imperfection in local exploitation, especially for problems with large design space and many design variables. An efficient adaptive SBO using fuzzy clustering algorithm for the infilling procedure is proposed in the paper. In each refinement cycle during SBO process, a Kriging model is constructed using the high-fidelity samples in current design space; then the current design space is divided into several subspaces using the fuzzy clustering algorithm with respect to the features of the objective function; hence new infilling samples are selected within each subspace and parallelly solved; thereafter, the current design space is updated by merging the subspaces. The proposed method is validated and assessed by several benchmark tests with bound constraints, further it is used for solving a beam optimization problem and an interstage-section optimization of a rocket. The results indicate the proposed method performs well both in local exploitation and global exploration, and is efficient in solving complex system optimizations.