Hybrid meta-model-based global optimum pursuing method for expensive problems

In this work, a hybrid meta-model-based global optimum pursuing (HMGOP) method is proposed for the expensive practical problems. In this method, a so-called important region is constructed using several expensive points. Three representative meta-models will then be used in both the important region and remaining region. A strategy to leave enough space for the remaining region has also been proposed to avoid the undesired points due to the narrow remaining region. The search process in the whole design space will also be carried out to further demonstrate the global optimum. Through test by several two-dimensional (2D) functions, each of which having several local optima, the proposed method shows great ability to escape the trap of the local optima. Through test with six high-dimensional problems, the proposed HMGOP method shows excellent search accuracy, efficiency, and robustness. Then, the proposed HMGOP method is applied in a vehicle lightweight design with 30 design variables, achieving satisfied results.