Optimal Experimental Design (D-Optimal, I-Optimal)
Also known as: D-Optimal Design, I-Optimal Design, Computer-Generated Design, Optimal Deneme Deseni (D-Optimal, I-Optimal)
Optimal experimental design is a computer-aided approach to constructing experiments that maximises statistical efficiency for a given model and run budget. Formalised by V. V. Fedorov in 1972, it selects experimental points from a candidate set so that the information matrix M = X'X is optimised according to a chosen criterion — most commonly D-optimality (maximising the determinant) or I-optimality (minimising average prediction variance). It is the preferred strategy whenever classical designs such as central composite or Box-Behnken cannot be applied because the experimental region is constrained or factor ranges are irregular.
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When to use it
Use optimal design when: (1) the experimental region is constrained and excludes many candidate factor combinations; (2) factor ranges are asymmetric or not amenable to classical two-level or three-level grids; (3) you need to fit a specific model form with a pre-determined, limited run count; or (4) mixture or process variables create an irregular design space. The method assumes the response surface model is correctly specified, that errors are approximately normally distributed with constant variance, and that the candidate point set adequately covers the feasible region. With at least ten runs the algorithm can produce reliable designs for moderate numbers of factors.
Strengths & limitations
- Handles constrained and irregular experimental regions where classical designs fail.
- Allows the researcher to specify the exact run count, making it compatible with tight budgets.
- Both D-optimal and I-optimal criteria are theoretically grounded and offer a quantifiable efficiency measure.
- Applicable to continuous and categorical factors simultaneously.
- Quality depends critically on the candidate point set and the starting design; a poor initial configuration may lead to a locally rather than globally optimal solution.
- D-optimal designs may cluster points at the extremes of the factor space, providing poor coverage for lack-of-fit testing unless replicate runs are explicitly requested.
- The design is optimal only for the pre-specified model; if the true response surface has a different form, efficiency can be substantially lower.
- Requires statistical software capable of running the exchange algorithm; manual construction is impractical.
Frequently asked
When should I choose D-optimal over I-optimal?
Choose D-optimal when your primary goal is to estimate model coefficients precisely — for example when you want to identify which factors matter most. Choose I-optimal when your goal is accurate prediction of the response across the entire design region, such as when building a surrogate model for optimisation.
How many runs do I need?
The minimum number of runs equals the number of model parameters (e.g. six for a full quadratic model in two factors). In practice you should add runs for pure-error replication (at least two to four additional runs at repeated settings) and ideally aim for 1.5 to 2 times the number of parameters to obtain reliable estimates.
Can I use optimal design with both continuous and categorical factors?
Yes. The coordinate-exchange algorithm handles mixed factor types by treating categorical factors as dummy variables and restricting candidate points to valid level combinations. This is one of the main advantages over classical factorial or central composite designs.
How do I know the resulting design is good enough?
Report the D-efficiency (for D-optimal) or the average variance of prediction (for I-optimal) relative to the theoretical best. A D-efficiency above 80–90% is generally considered adequate. You can also inspect the prediction variance surface to confirm coverage of the region of interest.
Sources
- Fedorov, V.V. (1972). Theory of Optimal Experiments. Academic Press. link ↗
- Atkinson, A.C., Donev, A.N., & Tobias, R.D. (2007). Optimum Experimental Designs, with SAS. Oxford University Press. ISBN: 978-0199296606
How to cite this page
ScholarGate. (2026, June 1). Optimal Experimental Design (D-Optimal, I-Optimal). ScholarGate. https://scholargate.app/en/experimental-design/optimal-design
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Box-Behnken DesignExperimental design↔ compare
- Central Composite DesignExperimental design↔ compare
- Full Factorial DesignExperimental design↔ compare
- Plackett-Burman DesignExperimental design↔ compare
- Response Surface MethodologyExperimental design↔ compare