Efficient adaptive response surface method using intelligent space exploration strategy

This article presents a novel intelligent space exploration strategy (ISES), which is then integrated with the adaptive response surface method (ARSM) for higher global optimization efficiency. ISES consists of two novel elements for space reduction and sequential sampling: i) Significant design space (SDS) identification algorithm, which is developed to identify the promising design space and balance local exploitation and global exploration during the search, and ii) An iterative maximin sequential Latin hypercube design (LHD) sampling scheme and tailored termination criteria. Moreover, an adaptive penalty method is developed for handling expensive constraints. The new global optimization strategy, notated as ARSM-ISES, is then tested with numerical benchmark problems on optimization efficiency, global convergence, robustness, and algorithm execution overhead. Comparative results show that ARSM-ISES not only outperforms the original ARSM and IARSM, in general it also converges to better optima with fewer function evaluations and less algorithm execution time as compared to state-of-the-art metamodel-based design optimization algorithms including MPS, EGO, and MSEGO. For high dimensional (HD) problems, ARSM-ISES shows promises as it performs better on chosen test problems than TR-MPS, which is especially designed for solving HD problems. ARSM-ISES is then applied to the optimal design of a lifting surface of hypersonic flight vehicles. Finally, main features and limitations of the proposed algorithm are discussed.