Constructing space-filling designs using an adaptive WSP algorithm for spaces with constraints

Abstract

Not all phenomena can be studied using standard experimental designs. Indeed, non-linear phenomena require experimental designs to cover the whole variable space in a reasonable number of experiments. Space-filling designs (SFD) propose a uniform distribution of points and are well adapted to numerical simulations. However, not all SFDs are equivalent in terms of uniformity of point distribution throughout the variable space, as assessed by quality criteria (such as MinDist, Coverage, etc.) and many algorithms which are powerful in low dimensional spaces (D<10) become difficult to use at higher dimensions (20D, 30D, etc.). The Wootton, Sergent, Phan-Tan-Luu's algorithm (WSP) was developed to select points from a set of candidate points and generate designs with good uniformity criteria whatever the number of dimensions. This study presents an adjustment of this algorithm, called adaptive WSP to obtain designs with specific experimental constraints, or when density is to be increased in a zone of particular interest. This adaptive WSP algorithm will be very useful as the number of dimensions increases and can solve the problem of the “hollow” center.