Optional reference point. If not provided the
maximum in each dimension is used.
Details
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.
Value
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.
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.
See Also
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.