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A Fast Way of Calculating Exact Hypervolumes

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3 Author(s)
While, L. ; Sch. of Comput. Sci. & Software Eng., Univ. of Western Australia, Perth, WA, Australia ; Bradstreet, L. ; Barone, L.

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.

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Evolutionary Computation, IEEE Transactions on  (Volume:16 ,  Issue: 1 )