IntersectionSet

(class from pyomo.contrib.pyros.uncertainty_sets)

class pyomo.contrib.pyros.uncertainty_sets.IntersectionSet(**unc_sets)

Bases: UncertaintySet

An intersection of a sequence of uncertainty sets, each of which is represented by an UncertaintySet object.

Parameters:

**unc_sets (dict) – PyROS UncertaintySet objects of which to construct an intersection. At least two uncertainty sets must be provided. All sets must be of the same dimension.

Examples

Intersection of origin-centered 2D box (square) and 2D hypersphere (circle):

>>> from pyomo.contrib.pyros import (
...     BoxSet, AxisAlignedEllipsoidalSet, IntersectionSet,
... )
>>> square = BoxSet(bounds=[[-1.5, 1.5], [-1.5, 1.5]])
>>> circle = AxisAlignedEllipsoidalSet(
...     center=[0, 0],
...     half_lengths=[2, 2],
... )
>>> # to construct intersection, pass sets as keyword arguments
>>> intersection = IntersectionSet(set1=square, set2=circle)
>>> intersection.all_sets
UncertaintySetList([...])

__init__(**unc_sets)

Initialize self (see class docstring).

Methods

__init__(**unc_sets)	Initialize self (see class docstring).
compute_auxiliary_uncertain_param_vals(point)	Compute auxiliary uncertain parameter values for a given point.
intersect(Q1, Q2)	Obtain the intersection of two uncertainty sets, accounting for the case where either of the two sets is discrete.
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 intersection 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

all_sets	List of the uncertainty sets of which to take the intersection.
dim	Dimension of the intersection set.
geometry	Geometry of the intersection set.
parameter_bounds	Uncertain parameter value bounds for the intersection set.
type	Brief description of the type of the uncertainty set.

Member Documentation

static intersect(Q1, Q2)

Obtain the intersection of two uncertainty sets, accounting for the case where either of the two sets is discrete.

Parameters:

• Q1 (UncertaintySet) – Operand uncertainty sets.

• Q2 (UncertaintySet) – Operand uncertainty sets.

Returns:

Intersection of the sets. A DiscreteScenarioSet is returned if both operand sets are DiscreteScenarioSet instances; otherwise, an IntersectionSet is returned.

Return type:

DiscreteScenarioSet or IntersectionSet

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 intersection 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 all_sets

List of the uncertainty sets of which to take the intersection. Must be of minimum length 2.

This attribute may be set through any iterable of UncertaintySet objects, and exhibits similar behavior to a list.

Type:

UncertaintySetList

property dim

Dimension of the intersection set.

Type:

int

property geometry

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

property parameter_bounds

Uncertain parameter value bounds for the intersection set.

Currently, an empty list, as the bounds cannot, in general, be computed without access to an optimization solver.

property type

Brief description of the type of the uncertainty set.

Type:

str