A novel extension algorithm for optimized Latin hypercube sampling

Latin hypercube sampling (LHS), as an efficient sampling method, has been widely used in computer experiments. But it is difficult to choice the sample size while applying LHS, especially for expensive simulations. The effective way is to add sample points sequentially. Nevertheless, the oversampling problem may be countered while extending the sample size with the existing extension algorithms of LHS. To alleviate this problem and obtain extension sample with good space-filling properties, a novel extension algorithm of optimized LHS (OLHS) is proposed. According to the extending rule, a new LHS is constructed by adding sample points of size n each time firstly. Then each additional sample points are optimized by the enhanced stochastic evolutionary algorithm based on the CL₂ space-filling criterion. The extension algorithm is illustrated by two test functions and appears to perform well in both efficiency and convergence compared with the traditional extension algorithm.