Fast construction of efficient two-level parallel flats designs

Abstract

Two-level parallel flats designs (PFDs) are nonregular designs that retain some of the simplicity of regular fractional factorial designs. PFDs have many desirable properties, such as flexible run sizes and block diagonal information matrices. In this article, we develop a fast algorithm for constructing efficient two-level PFDs, optimizing the parallel flats structure via a novel application of coordinate exchange. The resulting designs fill gaps among existing nonregular designs and outperform many comparably-sized designs in terms of G- and G2-aberration. An efficient implementation of the proposed algorithm in Matlab and GNU Octave can be found in the online Supplementary Material. Several new designs with desirable properties are generated and tabulated.