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Sliced Latin hypercube designs (SLHDs) are widely used in computerexperiments with both quantitative and qualitative factors and in batches.Optimal SLHDs achieve better space-filling property on the whole experimentalregion. However, most existing methods for constructing optimal SLHDs haverestriction on the run sizes. In this paper, we propose a new method forconstructing SLHDs with arbitrary run sizes, and a new combined space-fillingmeasurement describing the space-filling property for both the whole design andits slices. Furthermore, we develop general algorithms to search the optimalSLHD with arbitrary run sizes under the proposed measurement. Examples arepresented to illustrate that effectiveness of the proposed methods.

Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes