dominated_hypervolume calculates the dominated
hypervolume of the points in
1 2 3
Matrix containing the points one per column.
Optional reference point. If not provided the maximum in each dimension is used.
hypervolume_contribution calculates the
hypervolume contribution of each point.
If no reference point
ref is given, one is
automatically calculated by determening the maximum in
Currently only one general algorithm is implemented due to Fonseca et.al. but work is underway to include others such as the Beume & Rudolph approach as well as the approach by Bradstreet et.al.
The 1D and 2D cases are handle seperately by efficient
algorithms. Calculates the exact dominated hypervolume of
the points given in
x subject to the reference
dominated_hypervolume the dominated
hypervolume by the points in
points with respect
to the reference point
hypervolume_contribution a vector giving the
hypervolume soley dominated by that point.
Olaf Mersmann email@example.com
This code uses version 1.3 of the hypervolume code available from http://iridia.ulb.ac.be/~manuel/hypervolume. For a description of the algorithm see
Carlos M. Fonseca, Luis Paquete, and Manuel Lopez-Ibanez. An improved dimension-sweep algorithm for the hypervolume indicator. In IEEE Congress on Evolutionary Computation, pages 1157-1163, Vancouver, Canada, July 2006.
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