On supersaturated experimental design

In this article, optimization of a black box using designs of experiments is studied. There are two fundamental different branches in optimization using Design of Experiments; higher order Taylor expansions, i.e., response surface methodology, and underdetermined experimental designs, i.e., supersaturated designs. In this article, supersaturated designs are studied. Optimization using design of experiments is compared with direct search. A system of linear equations has to be solved, Ax = b, where A is the design matrix and b is a vector of experimental results. In supersaturated design, the solution x̂ to this system is not in general the gradient of the system but has a certain angle to it. This angle between the correct gradient, x, and the one found by supersaturated design of a linear approximation of a black box function, x̂, is investigated.