  Statistical design of experiments is widely used in scientific and industrial
investigations. A generalized minimum aberration (GMA) orthogonal array is
optimum under the well-established, so-called GMA criterion, and such an array
can extract as much information as possible at a fixed cost. Finding GMA arrays
is an open (yet fundamental) problem in design of experiments because
constructing such arrays becomes intractable as the number of runs and factors
increase. We develop two directed enumeration algorithms that call the integer
programming with isomorphism pruning algorithm of Margot (2007) for the purpose
of finding GMA arrays. Our results include 16 GMA arrays that were not
previously in the literature, along with documentation of the efficiencies that
made the required calculations possible within a reasonable budget of computer
time. We also validate heuristic algorithms against a GMA array catalog, by
showing that they quickly output near GMA arrays, and then use the heuristics
to find near GMA arrays when enumeration is computationally burdensome.
