  The best practical techniques for exact solution of instances of the
constrained maximum-entropy sampling problem, a discrete-optimization problem
arising in the design of experiments, are via a branch-and-bound framework,
working with a variety of concave continuous relaxations of the objective
function. A standard and computationally-important bound-enhancement technique
in this context is (ordinary) scaling, via a single positive parameter. Scaling
adjusts the shape of continuous relaxations to reduce the gaps between the
upper bounds and the optimal value. We extend this technique to generalized
scaling, employing a positive vector of parameters, which allows much more
flexibility and thus potentially reduces the gaps further. We give mathematical
results aimed at supporting algorithmic methods for computing optimal
generalized scalings, and we give computational results demonstrating the
performance of generalized scaling on benchmark problem instances.
