total_whv_rect#

moocore.total_whv_rect(x, /, rectangles, *, ref, maximise=False, ideal=None, scalefactor=0.1)[source]#

Compute total weighted hypervolume given a set of rectangles.

Calculates the hypervolume weighted by a set of rectangles (with zero weight outside the rectangles). The function total_whv_rect() calculates the total weighted hypervolume as hypervolume() + scalefactor * abs(prod(ref - ideal)) * whv_rect(). The details of the computation are given by Diaz and López-Ibáñez[1].

Warning

The current implementation only supports 2 objectives.

Parameters:

  • x – Numpy array of numerical values, where each row gives the coordinates of a point. If the array is created from the read_datasets() function, remove the last column.

  • rectangles – Weighted rectangles that will bias the computation of the hypervolume. Maybe generated by eafdiff() with rectangles=True or by choose_eafdiff().

  • ref – Reference point as a 1D vector. Must be same length as a single row in x.

  • maximise (bool or or list of bool) – Whether the objectives must be maximised instead of minimised. Either a single boolean value that applies to all objectives or a list of booleans, with one value per objective. Also accepts a 1D numpy array with values 0 or 1 for each objective.

  • ideal (default: None) – Ideal point as a vector of numerical values. If None, it is calculated as minimum (or maximum if maximising that objective) of each objective in the input data.

  • scalefactor (float, default: 0.1) – Real value within \((0,1]\) that scales the overall weight of the differences. This is parameter psi (\(\psi\)) in Diaz and López-Ibáñez[1].

Returns:

float – A single numerical value, the weighted hypervolume

See also

hypervolume, whv_rect, whv_hype

References

Examples

>>> rectangles = np.array(
...     [
...         [1.0, 3.0, 2.0, np.inf, 1],
...         [2.0, 3.5, 2.5, np.inf, 2],
...         [2.0, 3.0, 3.0, 3.5, 3],
...     ]
... )
>>> whv_rect([[2, 2]], rectangles, ref=6)
4.0
>>> whv_rect([[2, 1]], rectangles, ref=6)
4.0
>>> whv_rect([[1, 2]], rectangles, ref=6)
7.0
>>> total_whv_rect([[2, 2]], rectangles, ref=6, ideal=1)
26.0
>>> total_whv_rect([[2, 1]], rectangles, ref=6, ideal=1)
30.0
>>> total_whv_rect([[1, 2]], rectangles, ref=6, ideal=1)
37.5