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Mathematical Problems in Engineering
Volume 2015, Article ID 450492, 9 pages
Research Article

Two General Extension Algorithms of Latin Hypercube Sampling

Control and Simulation Center, Harbin Institute of Technology, Harbin 150080, China

Received 5 April 2015; Revised 30 June 2015; Accepted 8 July 2015

Academic Editor: Jose J. Muñoz

Copyright © 2015 Zhi-zhao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For reserving original sampling points to reduce the simulation runs, two general extension algorithms of Latin Hypercube Sampling (LHS) are proposed. The extension algorithms start with an original LHS of size and construct a new LHS of size that contains the original points as many as possible. In order to get a strict LHS of larger size, some original points might be deleted. The relationship of original sampling points in the new LHS structure is shown by a simple undirected acyclic graph. The basic general extension algorithm is proposed to reserve the most original points, but it costs too much time. Therefore, a general extension algorithm based on greedy algorithm is proposed to reduce the extension time, which cannot guarantee to contain the most original points. These algorithms are illustrated by an example and applied to evaluating the sample means to demonstrate the effectiveness.