hv_approx#

moocore.hv_approx(data, /, ref, maximise=False, nsamples=100000, seed=None, method='DZ2019')[source]#

Approximate the hypervolume indicator.

Approximate the value of the hypervolume metric with respect to a given reference point assuming minimization of all objectives. The default method="DZ2019" relies on Monte-Carlo sampling [1] and, thus, it gets more accurate, but slower, for higher values of nsamples.

See also

For details of the calculation, see Approximating the hypervolume metric.

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.

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

  • 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

  • nsamples (int, default: 100000) – Number of samples for Monte-Carlo sampling. Higher values give more accurate approximation of the true hypervolume but require more time.

  • seed (int | Generator | None, default: None) – Either an integer to seed numpy.random.default_rng(), Numpy default random number generator (RNG) or an instance of a Numpy-compatible RNG. None uses the equivalent of a random seed (see numpy.random.default_rng()).

  • method (Literal['DZ2019'], default: 'DZ2019') – Method to approximate the hypervolume.

Returns:

float – A single numerical value, the approximate hypervolume indicator.

References

Examples

>>> x = np.array([[5, 5], [4, 6], [2, 7], [7, 4]])
>>> moocore.hv_approx(x, ref=[10, 10], seed=42)
37.95471
>>> moocore.hypervolume(x, ref=[10, 10])
38.0

Merge all the sets of a dataset by removing the set number column:

>>> x = moocore.get_dataset("input1.dat")[:, :-1]

Dominated points are ignored, so this:

>>> moocore.hv_approx(x, ref=10, seed=42)
93.348976559100

gives the same hypervolume approximation as this:

>>> x = moocore.filter_dominated(x)
>>> moocore.hv_approx(x, ref=10, seed=42)
93.348976559100

The approximation is far from perfect for large sets:

>>> x = moocore.get_dataset("CPFs.txt")[:, :-1]
>>> x = moocore.filter_dominated(-x, maximise=True)
>>> x = moocore.normalise(x, to_range=[1, 2])
>>> reference = 0.9
>>> moocore.hypervolume(x, ref=reference, maximise=True)
1.0570447464301551
>>> moocore.hv_approx(x, ref=reference, maximise=True, seed=42)
1.056312559097445