A computational approach to optimal multivariate designs with respect to stratification and allocation is investigated under the assumptions of fixed total allocation, known number of strata, and the availability of administrative data correlated with thevariables of interest under coefficient-of-variation constraints. This approach uses a penalized objective function that is optimized by simulated annealing through exchanging sampling units and sample allocations among strata. Computational speed is improved through the use of a computationally efficient machine learning method such as K-means to create an initial stratification close to the optimal stratification. The numeric stability of the algorithm has been investigated and parallel processing has been employed where appropriate. Results are presented for both simulated data and USDA's June Agricultural Survey. An R package has also been made available for evaluation.

This article has an error and related omission in the literature review, as well as some errors in the specification of the simulation. Neither of these errors affect any results in the paper or conclusions drawn. The error and related omission in the literature review occur on page 122, paragraph 2. The reference, Lavallée and Hidiroglou (1988) is incorrect and should be replaced with a reference to Hidiroglou (1986). Both papers are similar in that they provide methods to optimally stratify and allocate univariate populations into take-all, take-none, and takesome stratum under a coefficient of variation (CV) constraint. However, Lavallée and Hidiroglou (1988) improves on Hidiroglou (1986) by allowing for an arbitrary number of take-some strata. This important contribution should have been included on page 122 paragraph 2, revised below.