在電腦實驗中，拉丁超立方設計（LHD）是一種常用的空間填充設計。此設計保證了設計點的一維投影有最佳的均勻度，但二維以上的投影則未必均勻。一種直接的改進辦法是使用特定均勻度準則對LHD做進一步挑選。本文考慮了近年提出的均勻投影準則，因為在此準則下的最優設計，會有良好的二維投影均勻度。利用迴歸分析中向前和逐步挑選法的概念，我們提出一演算法來搜尋均勻投影準則下最優的LHD。不同於現有的理論建構方法，我們對設計矩陣的大小並沒有特定的限制。並且透過簡單的模擬驗證，該演算法具有不錯的表現。隨著設計的規模增大，所有可能的設計數量增多時，演算法的效益也越明顯。

In computer experiments, Latin hypercube designs (LHDs) are commonly used space-filling designs. An LHD guarantees the best uniformity in all one-dimensional projections, but it may not enjoy a good uniformity in higher dimensional projections. In this paper, in order to construct designs that are space-filling in both one and two-dimensional projections, we use the uniform projection criterion to distinguish LHDs. Borrowing the concept of the forward and stepwise selection in regression analysis, we propose an algorithm to search for the optimal LHDs under the uniform projection criterion. Different from existing construction methods, our method has no restriction on the size of a design matrix. Some simulations are given to illustrate the performance of our algorithm.

目錄
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . .. . . . . 1
第二章定義和背景知識. . . . . . . . . . . . . . . . . . . . . . . .4
2.1 正交陣列及相關設計. . . . . . . . . . . . . . . . . . . . . . .5
2.2 均勻投影準則. . . . . . . . . . . . . . . . . . . . . . . . . .7
2.3 具良好二維均勻度的LHD . . . . . . . . . . . . . . . . . . . . .8
第三章演算法及結果. . . . . . . . . . . . . . . . . . . . . . . . .12
3.1 向前和逐步挑選法. . . . . . . . . . . . . . . . . . . . . . . .12
3.2 精簡宇集合. . . . . . . . . . . . . . . . . . . . . . . . . . .14
3.3 演算法表現驗證. . . . . . . . . . . . . . . . . . . . . . . . .15
3.3.1 與簡單隨機抽樣法比較. . . . . . . . . . . . . . . . . . . . .15
3.3.2 與OA-based LHD 比較. . . . . . . . . . . . . . . . . . . . . 16
第四章結論. . . . . . . . . . . . . . . . . . . . . . . .. . . . . 19
參考文獻. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . 20
附錄. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 22

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