A Fast Way of Calculating Exact Hypervolumes

We describe a new algorithm WFG for calculating hypervolume exactly. WFG is based on the recently-described observation that the exclusive hypervolume of a point
p
relative to a set
S
is equal to the difference between the inclusive hypervolume of
p
and the hypervolume of
S
with each point limited by the objective values in
p
. WFG applies this technique iteratively over a set to calculate its hypervolume. Experiments show that WFG is substantially faster (in five or more objectives) than all previously-described algorithms that calculate hypervolume exactly.