Reducing Symmetry in a Combinatorial Design Problem

A combinatorial design problem is considered which can be modelled as a constraint satisfaction problem in several diierent ways. The models all have a large number of symmetries which cause diiculties when searching for solutions. Diierent approaches to reducing the symmetry are discussed: remodelling the problem ; adding constraints to the model at the outset; and adding constraints during search to prevent symmetric assignments being explored on backtracking. The most successful strategy for the problem of this paper employs a complex model with less inherent symmetry than the others, combined with symmetry breaking during search.