Sobol Sequence Technique

The Sobol sequence provides a space-filling collection of points that are highly uniform in their spacing, as defined by measures of discrepancy. The uniformity of this technique generally improves on that of the Latin Hypercube technique, with similar cost in generation time. The Optimal Latin Hypercube technique provides greater point uniformity but at an increased cost in generation time; this cost can become prohibitively high for large numbers of points and factors.

Sobol sequences are deterministic, meaning that the first N design points for a given factor’s design space will be the same from study to study, even as you increase the number of points or change the number of factors. Despite this deterministic property, you can achieve diversity in your design points by using different skip value settings from one study to the next. Skip value settings, therefore, offer design study diversity and repeatability for this deterministic technique in a way similar to that of random seed settings in other pseudorandom techniques.

For example, if Total number of points is 20 and Number of initial Sobol points to be skipped is 500, the design matrix will contain 20 experiments numbered 501–520 out of the Sobol sequence set with 520 experiments.

User may optionally include corner points and baseline point in the design matrix. The technique also allows user to impose a constraint on factors. The constraint can be a function of one or more factors.