An efficient local search-based genetic algorithm for constructing optimal Latin hypercube design

Latin hypercube design (LHD) is a multi-stratified sampling method, which has been frequently used in sampling-based analysis. To achieve good space-filling quality of LHD, an efficient method, termed local search-based genetic algorithm (LSGA), is proposed in this article for constructing an optimal LHD. LSGA adopts modified order crossover, probabilistic mutation and adaptive selection operators to enrich population diversity and speed up convergence. A local search strategy is also presented in the approach to enhance the search ability. The performance of the proposed method is compared with several established methods in three perspectives, namely space-filling quality, computational efficiency and predictive accuracy of the metamodel. Several numerical experiments with distinct dimensions and numbers of design points are studied, and the results demonstrate that the proposed method performs better than other methods when dealing with LHD construction issues with high dimension and a large number of sampling points.