Optimal Design of Experiments is the construction of experimental designs that optimize a specific statistical criterion — using mathematical optimization to find the best possible set of experiments for a given model, constraints, and design size, rather than relying on classical factorial templates.

Key Optimality Criteria

• D-Optimal: Maximizes the determinant of $X^TX$ — minimizes the volume of the parameter confidence ellipsoid.
• A-Optimal: Minimizes the average variance of parameter estimates.
• I-Optimal: Minimizes the average prediction variance across the design space.
• G-Optimal: Minimizes the maximum prediction variance.

Why It Matters

• Irregular Regions: Works for constrained, non-rectangular parameter spaces where classical designs don't fit.
• Custom Models: Can design experiments for any specified model (non-standard terms, mixture models).
• Fewer Runs: Often achieves the same statistical power with fewer experiments than classical designs.

Optimal DOE is custom-tailored experiments — using math to design the statistically best possible experiment for your specific situation.