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Box-Behnken algorithm uses a selection of corner, face and central points to explore the experimental space with fewer points than a Full Factorial. It is similar to a Cubic Face Centered algorithm, but with the difference that no corner or extreme points are used. Box-Behnken experiments fill out a polyhedron, approximating a sphere.
The experiments are placed in the design variables hyper-cube as follows:
On the mid-points of each edge (2nvariables*nvariables).
On the hyper-cube's centre.
Hence the total number of designs is given by:
N=2(nvariables-1)*nvariables+1
Note that even if N is greater, the maximum number of generated designs is limited to 64000.
The following figure illustrates a Box-Behnken design space for three factors.
