Two-level Multi-surrogate Assisted Optimization method for high dimensional nonlinear problems

Curse of dimensionality is a key issue in engineering optimization. When the dimension increases, distribution of samples becomes sparse due to expanded design space. To obtain accurate and reliable results, the amount of samples often grows exponentially with the dimensions. To improve the efficiency of the surrogate with limited samples, a Two-level Multi-surrogate Assisted Optimization (TMAO) is suggested. The framework of the TMAO is to decompose a complicated problem into separable and non-separable components. In the first-level, High Dimensional Model Representation (HDMR) is utilized to determine the correlations among input variables. Then, a high dimensional problem can be decomposed into separable and non-separable components. Thus, the dimension of the original problem might be reduced significantly. Moreover, considering noises and outliers, Support Vector Regression (SVR)-HDMR is utilized to obtain more reliable surrogate. Expected Improvement (EI) criterion is suggested to generate new samples to save computational cost. In the second-level, to handle the non-separable component, a multi-surrogate assisted sampling strategy is suggested. Compared with other methods, the distinctive characteristic of the suggested sampling strategy is to use different surrogates to search potential uncertain regions. Considering the diversity of surrogates, more feature samples might be generated close to the local optimum. Even though it is still difficult to find a global solution, it could help us to find a feasible solution in practice. To verify the performance of the suggested method, several high dimensional mathematical functions are tested by the suggested method. The results demonstrate that all test functions can be successfully solved.