混料试验的D—最优对称设计,算法及应用

本文着重研究了混料试验的D—最优对称设计.基于Fedorov及Atwood的迭代方法,作者给出一个构造D—最优对称设计的改进算法.这个新算法由双循环迭代构成:从初始设计中减去最小方差对称点的设计测度;增加设计测度于最大方差的对称设计点,同时,本算法还只在对称子区域中寻找最大方差设计点,这样就使得Fedorov算法的收敛速度有了显著地提高,并能构造出更高效的D—最优对称设计.另外还给出一些构造实例.

D-OPTIMAL SYMMETRY DESIGNS FOR MIXTURE EXPERIMENTS, ALGORITHM AND ITS APPLICATION

In this paper, the D-optimal symmetry designs for mixture experiments is discussed. Based on the algorithms of Fedorov and Alwood, we advance an improved algorithm for constructing D-optimal symmetry design. This algorithm consists of two iterative processes, removing a measure from symmetry points of minimum variance in initial design and adding a measure to symmetry points of maximum variance. At the same time, the algorithm only finds the points of maximum variance in a symmetric subregion instead of the entire region. So that the rate of convergence of Fedorov's algorithm will be markedly improved and the more efficient approximate D-optimal symmetry designs will be obtained. In addition, some constructed examples are given.