  Volume is a natural geometric measure for comparing polyhedral relaxations of
non-convex sets. Speakman and Lee gave volume formulae for comparing
relaxations of trilinear monomials, quantifying the strength of various natural
relaxations. Their work was motivated by the spatial branch-and-bound algorithm
for factorable mathematical-programming formulations. They mathematically
analyzed an important choice that needs to be made whenever three or more terms
are multiplied in a formulation. We experimentally substantiate the relevance
of their main results to the practice of global optimization, by applying it to
difficult box cubic problems (boxcup). In doing so, we find that, using their
volume formulae, we can accurately predict the quality of a relaxation for
boxcups based on the (box) parameters defining the feasible region.
