CardinalitySet

(class from pyomo.contrib.pyros.uncertainty_sets)

class pyomo.contrib.pyros.uncertainty_sets.CardinalitySet(origin, positive_deviation, gamma)

Bases: UncertaintySet

A cardinality-constrained (i.e., “gamma”) set.

Parameters:

• origin ((N,) array_like) – Origin of the set (e.g., nominal uncertain parameter values).

• positive_deviation ((N,) array_like) – Maximal non-negative coordinate deviation from the origin in each dimension.

• gamma (numeric type) – Upper bound for the number of uncertain parameters which may realize their maximal deviations from the origin simultaneously.

Examples

A 3D cardinality set:

>>> from pyomo.contrib.pyros import CardinalitySet
>>> gamma_set = CardinalitySet(
...     origin=[0, 0, 0],
...     positive_deviation=[1.0, 2.0, 1.5],
...     gamma=1,
... )
>>> gamma_set.origin
array([0, 0, 0])
>>> gamma_set.positive_deviation
array([1. , 2. , 1.5])
>>> gamma_set.gamma
1

__init__(origin, positive_deviation, gamma)

Initialize self (see class docstring).

Methods

__init__(origin, positive_deviation, gamma)	Initialize self (see class docstring).
compute_auxiliary_uncertain_param_vals(point)	Compute auxiliary uncertain parameter values for a given point.
is_bounded(config)	Determine whether the uncertainty set is bounded.
is_nonempty(config)	Return True if the uncertainty set is nonempty, else False.
is_valid(config)	Return True if the uncertainty set is bounded and non-empty, else False.
point_in_set(point)	Determine whether a given point lies in the cardinality set.
set_as_constraint([uncertain_params, block])	Construct a block of Pyomo constraint(s) defining the uncertainty set on variables representing the uncertain parameters, for use in a two-stage robust optimization problem or subproblem (such as a PyROS separation subproblem).

Attributes

dim	Dimension N of the cardinality set.
gamma	Upper bound for the number of uncertain parameters which may maximally deviate from their respective origin values simultaneously.
geometry	Geometry of the cardinality set.
origin	Origin of the cardinality set (e.g. nominal parameter values).
parameter_bounds	Bounds in each dimension of the cardinality set.
positive_deviation	Maximal coordinate deviations from the origin in each dimension.
type	Brief description of the type of the uncertainty set.

Member Documentation

compute_auxiliary_uncertain_param_vals(point, solver=None)

Compute auxiliary uncertain parameter values for a given point. The point need not be in the uncertainty set.

Parameters:

• point ((N,) array-like) – Point of interest.

• solver (Pyomo solver, optional) – If needed, a Pyomo solver with which to compute the auxiliary values.

Returns:

aux_space_pt – Computed auxiliary uncertain parameter values.

Return type:

numpy.ndarray

is_bounded(config)

Determine whether the uncertainty set is bounded.

Parameters:

config (ConfigDict) – PyROS solver configuration.

Returns:

True if the uncertainty set is certified to be bounded, and False otherwise.

Return type:

bool

Notes

This check is carried out by solving a sequence of maximization and minimization problems (in which the objective for each problem is the value of a single uncertain parameter). If any of the optimization models cannot be solved successfully to optimality, then False is returned.

This method is invoked during the validation step of a PyROS solver call.

is_nonempty(config)

Return True if the uncertainty set is nonempty, else False.

is_valid(config)

Return True if the uncertainty set is bounded and non-empty, else False.

point_in_set(point)

Determine whether a given point lies in the cardinality set.

Parameters:

point ((N,) array-like) – Point (parameter value) of interest.

Returns:

True if the point lies in the set, False otherwise.

Return type:

bool

set_as_constraint(uncertain_params=None, block=None)

Construct a block of Pyomo constraint(s) defining the uncertainty set on variables representing the uncertain parameters, for use in a two-stage robust optimization problem or subproblem (such as a PyROS separation subproblem).

Parameters:

• uncertain_params (None, Var, or list of Var, optional) – Variable objects representing the (main) uncertain parameters. If None is passed, then new variable objects are constructed.

• block (BlockData or None, optional) – Block on which to declare the constraints and any new variable objects. If None is passed, then a new block is constructed.

Returns:

A collection of the components added or addressed.

Return type:

UncertaintyQuantification

property dim

Dimension N of the cardinality set.

Type:

int

property gamma

Upper bound for the number of uncertain parameters which may maximally deviate from their respective origin values simultaneously. Must be a numerical value ranging from 0 to the set dimension N.

Note that, mathematically, setting gamma to 0 reduces the set to a singleton containing the center, while setting gamma to the set dimension N makes the set mathematically equivalent to a BoxSet with bounds numpy.array([origin, origin + positive_deviation]).T.

Type:

numeric type

property geometry

Geometry of the cardinality set. See the Geometry class documentation.

property origin

Origin of the cardinality set (e.g. nominal parameter values).

Type:

(N,) numpy.ndarray

property parameter_bounds

Bounds in each dimension of the cardinality set.

Returns:

List, length N, of 2-tuples. Each tuple specifies the bounds in its corresponding dimension.

Return type:

list of tuples

property positive_deviation

Maximal coordinate deviations from the origin in each dimension. All entries are nonnegative.

Type:

(N,) numpy.ndarray

property type

Brief description of the type of the uncertainty set.

Type:

str