dominated_hypervolume calculates the dominated
hypervolume of the points in points.
dominated_hypervolume(points, ref)
hypervolume_contribution(points, ref)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.
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.
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.