moocore.

total_whv_rect#

moocore.total_whv_rect(points, /, 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:

  • points (ArrayLike) – Array of numerical values, where each row gives the coordinates of a point in objective space. If the array is created by the read_datasets() function, remove the last column.

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

  • ref (ArrayLike) – Reference point as a 1D vector. Must be either a single value, which will be used for all coordinates, or the same length as a single point in points.

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

  • ideal (ArrayLike | None, 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 points.

  • 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
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