A fast optimal Latin hypercube design method using an improved translational propagation algorithm

To further improve the space-filling quality and computational efficiency of the translational propagation algorithm, especially for high-dimensional and large-scale sampling problems, this article presents an improved translational propagation algorithm (iTPA). First, a novel uniform translating process is proposed to better allocate sample points. Second, the resizing process is improved to relieve its adverse influence on the space-filling quality. Comparative studies demonstrate the appealing merits of iTPA: (i) iTPA generally outperforms the existing optimization-based Latin hypercube design (LHD) methods; (ii) for high-dimensional and large-scale sampling problems, the computational efficiency of iTPA is dramatically improved and insensitive to sampling dimension and scale; (iii) iterations of iTPA can be used to enrich available LHDs and further upgrade the space-filling quality. Finally, an engineering example is presented to demonstrate the benefit of iTPA in improving the accuracy of surrogates.