A.7 Choice of a design

A.7.1 Random search

We begin by recalling that group theory can be used to determine directly an optimal design when $\Omega$ is indeed a product space. When phase asserting removes a significant proportion of possibilities, finding an optimal design is more difficult.

LISTING 19 selects a design at random... providing that its determinant doesnt vanish. By iteration, one obtains a "not so bad design" (LISTING 20).

A.7.2 Directed search

LISTING 21 gives matrix $mT$ relative to the full factorial design.

Given a DOE $mA$ and its associated symmetric matrix $mS$, LISTING 22 computes the most distant experiment, i.e. the experiment in $\Omega\setminus\omega$ for which the estimated error is the most important. When several experiments are realizing the maximal error, one of them is chosen at random.

Doing one step is as follows (LISTING 23) : start form a given $mA$ and $mS$. Add the most distant experiment, and determines (by trial and error) wich experiment to remove from the list in order to decrease the masimal error. When this algorithm succeds, iterate one step more.

Doing several steps is as follows (LISTING 24) : start from a random point and improve as much as you can. Then pick another random starting point and so one. Stop when reaching the number of tries.