Model-robust two-level designs using coordinate exchange algorithms and a maximin criterion

We propose a candidate-list-free exchange algorithm that facilitates construction of exact, model-robust, two-level experiment designs. In particular, we investigate two model spaces previously considered in the literature. The first assumes that all main effects and an unknown subset of two-factor interactions are active, but that the experimenter knows the number of active interactions. The second assumes that an unknown subset of the main effects, and all associated two-factor interactions, are active. Previous literature uses two criteria for design construction: first, maximize the number of estimable models; then, differentiate between designs equivalent in estimability by choosing the design with the highest average D-efficiency. We adopt a similar strategy, but (1) do not impose orthogonality or factor level balance constraints, resulting in generally equal or larger numbers of estimable models, and (2) use a flexible secondary criterion that maximizes the minimum D-efficiency. We provide results for many situations of interest. We also provide online supplementary material that includes algorithmic details, designs, and MATLAB code.