A multi-point sampling method based on kriging for global optimization

In general, sampling strategy plays a very important role in metamodel based design optimization, especially when computationally expensive simulations are involved in the optimization process. The research on new optimization methods with less sampling points and higher convergence speed receives great attention in recent years. In this paper, a multi-point sampling method based on kriging (MPSK) is proposed for improving the efficiency of global optimization. The sampling strategy of this method is based on a probabilistic distribution function converted from the expected improvement (EI) function. It can intelligently draw appropriate new samples in an area with certain probability according to corresponding EI values. Besides, three strategies are also proposed to speed up the sequential sampling process and the corresponding convergence criterions are put forward to stop the searching process reasonably. In order to validate the efficiency of this method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the higher global optimization efficiency of this method makes it particularly suitable for design optimization problems involving computationally expensive simulations.