Whole-Plot Exchange Algorithms for Constructing D-Optimal Multistratum Designs

Multistratum experiments contain several different sizes of experimental units. Examples include split-plot, strip-plot designs, and randomized block designs. We propose a strategy for constructing a D-optimal multistratum design by improving a randomly generated design through a sequence of whole-plot exchanges. This approach preserves the design structure and simplifies updates to the information and is applicable to any multistratum design where the largest-sized experimental unit is either a whole plot or a block. Two whole-plot exchange algorithms inspired by the point-exchange strategies of Fedorov (1972 Fedorov , V. V. ( 1972 ). Theory of Optimal Experiments . New York : Academic Press . [Google Scholar]) and Wynn (1972 Wynn , H. P. ( 1972 ). Results in the theory and construction of D-optimum experimental designs . Journal of the Royal Statistical Society Series B Statistics Methodology 34 : 133 – 147 . [Google Scholar]) are described. The application of the algorithms to several design problems is discussed.