dominated_hypervolume {emoa}R Documentation

Dominated Hypervolume calculation


dominated_hypervolume calculates the dominated hypervolume of the points in points.


  dominated_hypervolume(points, ref)

  hypervolume_contribution(points, ref)



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 each coordinate.

Currently only one general algorithm is implemented due to Fonseca but work is underway to include others such as the Beume & Rudolph approach as well as the approach by Bradstreet

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.


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.


Olaf Mersmann


This code uses version 1.3 of the hypervolume code available from 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.

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.

[Package emoa version 0.5-0.1 Index]