RelativeHypervolume#

class moocore.RelativeHypervolume(ref, ref_set, maximise=False)[source]#

Computes the hypervolume value of fronts relative to the hypervolume of a reference front.

The value is computed as \(1 - \frac{\text{hyp}(X)}{\text{hyp}(R)}\), where \(X\) is an input set (front), \(R\) is the reference front and \(\text{hyp}()\) is calculated by hypervolume(). Thus, lower values are better, in contrast to the usual hypervolume. The metric has also been called hypervolume relative deviation [1].

Parameters:

  • ref (ArrayLike) – Reference point as a 1D vector. Must be same length as a single point in ref_set.

  • ref_set (ArrayLike) – Reference set (front) as 2D array. The reference front does not need to weakly dominate the input sets. If this is required, the user must ensure it.

  • maximise (bool | list[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 booleans, with one value per objective. Also accepts a 1D numpy array with value 0/1 for each objective.

References

Examples

Default is minimization, we can easily assume maximization.

>>> ref_set = [[6, 6], [2, 7], [7, 2]]
>>> hv_ind = moocore.RelativeHypervolume(ref=0, ref_set=ref_set, maximise=True)
>>> hv_ind([[5, 5], [4, 6], [2, 7], [7, 4]])
0.0250000
>>> hv_ind([[5, 5], [4, 6], [7, 4]])
0.0749999
>>> hv_ind([[0, 0]])
1.0
>>> hv_ind(ref_set)
0.0
__call__(data)[source]#

Compute relative hypervolume indicator as 1 - (hypervolume(data, ref=ref) / hypervolume(ref_set, ref=ref)).

Parameters:

data (ArrayLike) – 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.

Returns:

float – A single numerical value, the relative hypervolume indicator, which must be minimized.