dominated_hypervolume calculates the dominated hypervolume of
the points in points.
dominated_hypervolume(points, ref)hypervolume_contribution(points, ref)
For dominated_hypervolume the dominated hypervolume
by the points in points with respect to the reference point
ref. For hypervolume_contribution a vector giving
the hypervolume soley dominated by that point.
Matrix containing the points one per column.
Optional reference point. If not provided the maximum in each dimension is used.
Olaf Mersmann olafm@statistik.tu-dortmund.de
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 each coordinate.
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 point ref.
This code uses version 1.3 of the hypervolume code available from https://lopez-ibanez.eu/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.
nondominated_points to extract the pareto
front approximation from a given set of points and
nds_hv_selection for a selection strategy based on
the hypervolume contribution of each point.