Functions for the calculation of the dominated hypervolume (contribution).

The function computeHV computes the dominated hypervolume of a set of points given a reference set whereby computeHVContr computes the hypervolume contribution of each point.

If no reference point is given the nadir point of the set x is determined and a positive offset with default 1 is added. This is to ensure that the reference point dominates all of the points in the reference set.

computeHV(x, ref.point = NULL)

computeHVContr(x, ref.point = NULL, offset = 1)

Arguments

x	[matrix] Matrix of points (column-wise).
ref.point	[numeric | NULL] Reference point. Set to the maximum in each dimension by default if not provided.
offset	[numeric(1)] Offset to be added to each component of the reference point only in the case where no reference is provided and one is calculated automatically.

Value

[numeric(1)] Dominated hypervolume in the case of computeHV and the dominated hypervolume contributions for each point in the case of computeHVContr.

Note

: Keep in mind that this function assumes all objectives to be minimized. In case at least one objective is to be maximized the matrix x needs to be transformed accordingly in advance.