Constructing uniform designs: A heuristic integer programming method

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• 作者：Yong-Dao Zhou^a ; ^{ydzhou@scu.edu.cn} ; Kai-Tai Fang^b ; ^c ; ^{ktfang@uic.edu.hk} ; Jian-Hui Ning^d ; ^{jhning@mail.ccnu.edu.cn}
• 关键词：Quadratic integer programming ; Simulated annealing ; Uniform design ; Wrap-around L2-discrepancy
• 刊名：Journal of Complexity
• 出版年：2012
• 期刊代码：73_0885064x
• 类别：mt
• 出版时间：April, 2012
• 卷：28
• 期：2
• 页码：224-237
• 文件大小：411 K

摘要

In this paper, the wrap-around -discrepancy (WD) of asymmetrical design is represented as a quadratic form, thus the problem of constructing a uniform design becomes a quadratic integer programming problem. By the theory of optimization, some theoretic properties are obtained. Algorithms for constructing uniform designs are then studied. When the number of runs is smaller than the number of all level-combinations , the construction problem can be transferred to a zero-one quadratic integer programming problem, and an efficient algorithm based on the simulated annealing is proposed. When , another algorithm is proposed. Empirical study shows that when is large, the proposed algorithms can generate designs with lower WD compared to many existing methods. Moreover, these algorithms are suitable for constructing both symmetrical and asymmetrical designs.