  In this paper, we demonstrate that considering experiments in a
graph-theoretic manner allows us to exploit automorphisms of the graph to
reduce the number of evaluations of candidate designs for those experiments,
and thus find optimal designs faster. We show that the use of automorphisms for
reducing the number of evaluations required of an optimality criterion function
is effective on designs where experimental units have a network structure.
Moreover, we show that we can take block designs with no apparent network
structure, such as one-way blocked experiments, row-column experiments, and
crossover designs, and add block nodes to induce a network structure.
Considering automorphisms can thus reduce the amount of time it takes to find
optimal designs for a wide class of experiments.
