Integer Programming for Enumerating Orthogonal Arrays Article Swipe
Statistical design of experiments is widely used in scientific and industrial investigations. An optimum orthogonal array can extract as much information as possible at a fixed cost. Finding (optimum) orthogonal arrays is an open (yet fundamental) problem in design of experiments because constructing (optimum) orthogonal arrays or proving non-existence becomes intractable as the number of runs and factors increase. Enumerating orthogonal arrays is equivalent to finding all feasible solutions to a class of inherently symmetric constraint satisfaction problems. The inherent symmetry implies that the solutions remain feasible under the action of a group permuting the variables. This causes the number of feasible solutions to be huge. We develop algorithms for enumerating orthogonal arrays that call the Margot (2007) isomorphism pruning algorithm and bring the enumeration of OA(160, k, 2, 4) for k = 9, 10 and OA(176, k, 2, 4) for k = 8, 9, 10 within computational reach. A catalog of the newly found optimum orthogonal arrays obtained using our algorithms is also presented.
