A Fast Way of Calculating Exact Hypervolumes

Authors:
Lyndon While;Lucas Bradstreet;Luigi Barone
Affiliations:
School of Computer Science and Software Engineering, University of Western Australia, Perth, Australia;School of Computer Science and Software Engineering, University of Western Australia, Perth, Australia;School of Computer Science and Software Engineering, University of Western Australia, Perth, Australia
Venue:
IEEE Transactions on Evolutionary Computation
Year:
2012

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Abstract

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.