Hypervolume utilities#

class pygmo.hypervolume(points)#

Hypervolume Class

Constructor from points

Parameters: points (2d array-like object) – the points
Raises: ValueError – if points is inconsistent

Examples

>>> from pygmo import *
>>> points = [[1,2],[0.5, 3],[0.1,3.1]]
>>> hv = hypervolume(points = points)

See also the docs of the C++ class pagmo::hypervolume.

__init__(pop)

Constructor from population

Parameters: pop (population) – the input population
Raises: ValueError – if pop contains a single-objective or a constrained problem

Examples

>>> from pygmo import *
>>> pop = population(prob = zdt(prob_id = 1), size = 20)
>>> hv = hypervolume(pop = pop)

See also the docs of the C++ class pagmo::hypervolume.

compute(ref_point, hv_algo=auto)#

Computes the hypervolume with the supplied algorithm. If no algorithm is supplied, then an exact hypervolume algorithm is automatically selected specific for the point dimension.

Parameters

ref_point (2d array-like object) – the points
hv_algo (deriving from _hv_algorithm) – hypervolume algorithm to be used

Returns

the computed hypervolume assuming ref_point as reference point

Return type

float

Raises

ValueError – if ref_point is not dominated by the nadir point

See also the docs of the C++ class pagmo::hypervolume::compute().

contributions(ref_point, hv_algo=auto)#

This method returns the exclusive contribution to the hypervolume of every point. According to hv_algo this computation can be implemented optimally (as opposed to calling for exclusive() in a loop).

Parameters

ref_point (2d array-like object) – the points
hv_algo (deriving from _hv_algorithm) – hypervolume algorithm to be used

Returns

the contribution of all points to the hypervolume

Return type

1D NumPy float array

Raises

ValueError – if ref_point is not suitable

See also the docs of the C++ class pagmo::hypervolume::contributions().

exclusive(idx, ref_point, hv_algo=auto)#

Computes the exclusive contribution to the hypervolume of a particular point.

Parameters

idx (int) – index of the point
ref_point (array-like object) – the reference point
hv_algo (deriving from _hv_algorithm) – hypervolume algorithm to be used

Returns

the contribution of all points to the hypervolume

Return type

1D NumPy float array

Raises

ValueError – if ref_point is not suitable or if idx is out of bounds
OverflowError – if idx is negative or greater than an implementation-defined value

See also the docs of the C++ class pagmo::hypervolume::exclusive().

greatest_contributor(ref_point, hv_algo=auto)#

Computes the point contributing the most to the total hypervolume.

Parameters

ref_point (array-like object) – the reference point
hv_algo (deriving from _hv_algorithm) – hypervolume algorithm to be used

Raises

ValueError – if ref_point is not suitable

See also the docs of the C++ class pagmo::hypervolume::greatest_contributor().

least_contributor(ref_point, hv_algo=auto)#

Computes the point contributing the least to the total hypervolume.

Parameters

ref_point (array-like object) – the reference point
hv_algo (deriving from _hv_algorithm) – hypervolume algorithm to be used

Raises

ValueError – if ref_point is not suitable

See also the docs of the C++ class pagmo::hypervolume::least_contributor().

refpoint(offset=0)#

Calculates a mock refpoint by taking the maximum in each dimension over all points saved in the hypervolume object. The result is a point that is necessarily dominated by all other points, and thus can be used for hypervolume computations.

This point is different from the one computed by nadir() as only the non dominated front is considered in that method (also its complexity is thus higher)

Parameters: offset (float) – the reference point
Returns: the reference point
Return type: 1D NumPy float array

See also the docs of the C++ class pagmo::hypervolume::refpoint().

class pygmo.hvwfg(stop_dimension=2)#

The hypervolume algorithm from the Walking Fish Group (2011 version).

This object can be passed as parameter to the various methods of the class hypervolume as it derives from the hidden base class _hv_algorithm

Parameters: stop_dimension (int) – the input population
Raises: OverflowError – if stop_dimension is negative or greater than an implementation-defined value

Examples

>>> import pygmo as pg
>>> hv_algo = pg.hvwfg(stop_dimension = 2)

See also the docs of the C++ class pagmo::hvwfg.

class pygmo.hv2d#

Exact hypervolume algorithm for two dimensional points.

This object can be passed as parameter to the various methods of the class hypervolume as it derives from the hidden base class _hv_algorithm

Examples

>>> import pygmo as pg
>>> hv_algo = pg.hv2d()

See also the docs of the C++ class pagmo::hv2d.

class pygmo.hv3d#

Exact hypervolume algorithm for three dimensional points.

This object can be passed as parameter to the various methods of the class hypervolume as it derives from the hidden base class _hv_algorithm

Examples

>>> import pygmo as pg
>>> hv_algo = pg.hv3d()

See also the docs of the C++ class pagmo::hv3d.

class pygmo.bf_fpras(eps=1e-2, delta=1e-2, seed=random)#

Bringmann-Friedrich approximation method. Implementation of the Bringmann-Friedrich approximation scheme (FPRAS), reduced to the special case of approximating the hypervolume indicator.

This object can be passed as parameter to the various methods of the class hypervolume as it derives from the hidden base class _hv_algorithm

Examples

>>> import pygmo as pg
>>> hv_algo = pg.bf_fpras(eps = 1e-2, delta = 1e-2)

See also the docs of the C++ class pagmo::bf_fpras.

class pygmo.bf_approx#

Bringmann-Friedrich approximation method. Implementation of the Bringmann-Friedrich approximation scheme (FPRAS), reduced to the special case of approximating the least contributor.

This object can be passed as parameter to the various methods of the class hypervolume as it derives from the hidden base class _hv_algorithm

Examples

>>> import pygmo as pg
>>> hv_algo = pg.bf_approx()

See also the docs of the C++ class pagmo::bf_approx.