Optimization-Assisted Fractional Factorial Design
Also known as: optimal fractional factorial design, algorithmically optimized FFD, computer-aided fractional factorial design, D-optimal fractional factorial design
Optimization-assisted fractional factorial design (OA-FFD) combines classical fractional factorial screening with algorithmic optimality criteria — such as D-, I-, or A-optimality — to construct experiment matrices that maximize statistical efficiency. Instead of relying solely on standard orthogonal-array tables, a computer algorithm selects the best subset of runs from a candidate set, enabling experimenters to handle irregular factor constraints, mixed factor types, and custom run sizes that standard tables cannot accommodate.
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When to use it
Use optimization-assisted FFD when standard orthogonal-array tables do not fit your situation: factors have different numbers of levels, some run combinations are infeasible, the budget dictates a non-standard number of runs, or both continuous and categorical factors must appear in the same design. It is especially valuable in early-phase engineering screening studies with 5–20 factors when a full factorial is too expensive and standard tables are too rigid. Do NOT use it when a standard fractional factorial table fits exactly — the additional computational complexity is unnecessary and the catalog design will often be equally efficient. Also avoid it when no subject-matter model can be specified in advance; the algorithm optimizes for a declared model, so a wrong model specification produces a design that is efficient for the wrong question.
Strengths & limitations
- Handles irregular constraints, mixed factor types, and arbitrary run sizes that standard catalog designs cannot accommodate.
- Maximizes statistical efficiency for the experimenter's specific model, often achieving near-orthogonal structure under real-world constraints.
- Embeds feasibility constraints directly into design construction, so all planned runs are executable.
- Supported by mature software (JMP, SAS Proc Optex, R AlgDesign, Python pyDOE2), lowering the barrier to application.
- Applicable across engineering, manufacturing, pharmaceutical development, and any domain with custom experimental constraints.
- Requires specifying the intended model before data collection; if the true model differs, the optimized design may perform poorly for the actual analysis.
- D-optimal or I-optimal designs are not guaranteed to be orthogonal; mild correlations among factor estimates may remain.
- The coordinate-exchange algorithm finds a local optimum; multiple random starts are needed to improve confidence that a global optimum was reached.
- Harder to explain and justify to non-technical stakeholders compared with a standard 2^(k-p) design from a published table.
Frequently asked
When should I use a D-optimal design instead of a standard 2^(k-p) fractional factorial?
Use a D-optimal (optimization-assisted) design when your factors have different numbers of levels, some level combinations are infeasible, the desired run count is not a power of two, or you need to estimate a specific set of interaction terms that standard resolutions do not support cleanly. If a standard table fits your situation, use it — catalog designs are simpler to explain and often equally efficient.
What software can I use to generate an optimization-assisted fractional factorial design?
JMP (Custom Design platform), SAS (Proc Optex), R (AlgDesign package, skpr package), Python (pyDOE2), and Minitab (Response Optimizer with custom designs) all implement coordinate-exchange or Federov-exchange algorithms for D- and I-optimal design generation.
How many random starts should I use in the coordinate-exchange algorithm?
There is no universal rule, but 10–50 random starts is a commonly recommended minimum. Compare the D-efficiency across starts and select the design with the highest value. For large factor spaces or heavily constrained problems, more starts improve confidence that a near-global optimum has been found.
Is an optimization-assisted design always better than a standard fractional factorial?
Not necessarily. When a standard 2^(k-p) design with the required resolution exists and no constraints apply, the catalog design is equally efficient and much easier to explain. Optimization-assisted designs add value specifically when constraints, mixed factor types, or non-standard run counts make catalog designs inapplicable or inefficient.
Can I add center points to an optimization-assisted fractional factorial design?
Yes. Center points can be added manually after the optimization step to provide a model-independent check for curvature. Alternatively, I-optimal or Bayesian D-optimal criteria can be used during design construction to explicitly account for potential quadratic effects, effectively embedding curvature detection into the optimized design.
Sources
- Atkinson, A. C., Donev, A. N., & Tobias, R. D. (2007). Optimum Experimental Designs, with SAS. Oxford University Press. ISBN: 978-0199296606
- Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). Wiley. ISBN: 978-1119320937
How to cite this page
ScholarGate. (2026, June 3). Optimization-Assisted Fractional Factorial Design. ScholarGate. https://scholargate.app/en/experimental-design/optimization-assisted-fractional-factorial-design
Which method?
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