D-optimal Design

Algorithmically generated design that maximises the determinant of the information matrix $X^{⊤} X$ — for situations no standard design fits.

Also known as: D-optimal, D-optimum design

A D-optimal design is assembled from a candidate set by an optimisation algorithm (coordinate exchange, Fedorov, modified Fedorov) that maximises the D-efficiency — a measure of regression-coefficient precision.

D-efficiency = (\frac{∣ X ^{⊤} X ∣}{N ^{p}})^{1/ p}

Free run count — arbitrary number of runs, not tied to $2^{k}$ or $2^{k} + 2 k$
Non-standard factor spaces — usable with irregular feasible regions or forbidden combinations
Mixed factor types — continuous, categorical, mixed, different level counts

Used in

In the Algorithm Lab

Sources

Atkinson, A. C., Donev, A. N. & Tobias, R. D. — Optimum Experimental Designs, with SAS, Oxford University Press, 2007
Goos, P. & Jones, B. — Optimal Design of Experiments: A Case Study Approach, Wiley, 2011
Montgomery, D. C. — Design and Analysis of Experiments, 10th Edition, Chapter 11