A Rapid Mode Pursuing Sampling Method for High Dimensional Optimization Problems

Approximate optimization strategies using design of computer experiments (DoCE) and metamodels have been widely applied in design of modern complex engineering systems. Mode pursuing sampling method (MPS) is a representative of such optimization algorithms. A rapid mode pursuing sampling method using significant design space concept (notated as RMPS-SDS) is proposed in this work to alleviate the low efficiency problem of MPS in solving high dimensional optimization problems. The idea of significant design space is incorporated into the MPS framework, and a sample point allocation strategy is designed to enhance the local search capability and convergence speed of MPS. RMPS-SDS is tested on a number of standard numerical benchmark problems and two engineering design problems and compared with MPS and GA. The comparison results indicate that with the same computational budget (i. e., the same number of function evaluations), results of RMPS-SDS are much closer to the theoretical global optima with lower standard deviation for multiple runs. It is thus demonstrated that the proposed RMPS-SDS outperforms the standard MPS in terms of efficiency, convergence, and robustness in solving high dimensional optimization problems, which is more promising for engineering practices. © 2019 Journal of Mechanical Engineering.