Alejandro S. Hernandez
Abstract
We present a new method for constructing nearly orthogonal Latin hypercubes that greatly expands their availability to experimenters. Latin hypercube designs have proven useful for exploring complex, high-dimensional computational models, but can be plagued with unacceptable correlations among input variables. To improve upon their effectiveness, many researchers have developed algorithms that generate orthogonal and nearly orthogonal Latin hypercubes. Unfortunately, these methodologies can have strict limitations on the feasible number of experimental runs and variables. To overcome these restrictions, we develop a mixed integer programming algorithm that generates Latin hypercubes with little or no correlation among their columns for most any determinate run-variable combination—including fully saturated designs. Moreover, many designs can be constructed for a specified number of runs and factors—thereby providing experimenters with a choice of several designs. In addition, our algorithm can be used to quickly adapt to changing experimental conditions by augmenting existing designs by adding new variables or generating new designs to accommodate a change in runs.
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Index Terms
- Constructing nearly orthogonal latin hypercubes for any nonsaturated run-variable combination
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