Being on the Cutting Edge

Cutters of diamonds and other gemstones have a high-pressure job
with conflicting demands: Flaws must be removed from rough stones
to maximize brilliance but done so in a way that yields the
greatest weight possible. Because diamonds are often cut to a
standard shape, cutting them is far less complex than cutting other
gemstones, such as rubies or sapphires, which can have hundreds of
different shapes. By coupling geometry and multivariable calculus
with optimization techniques, mathematicians have been able to
devise algorithms that automatically generate precise cutting plans
that maximize brilliance and yield. The goal is to find the final
shape within a rough stone. There are an endless number of
candidates, positions, and orientations, so finding the shape
amounts to a maximization problem with a large number of variables
subject to an infinite number of constraints, a technique called
semi-infinite optimization. Experienced human cutters create
finished gems that average about 1/3 of the weight of the original
rough stone. Cutting with this automated algorithm improved the
yield to well above 40%, which, given the value of the stones, is a
tremendous improvement. Without a doubt, semi-infinite optimization
is a girl.s (or boy.s) best friend.