commonpower.modeling.mip_builder.MIPExpressionBuilder

class MIPExpressionBuilder(entity: ModelEntity, M: int = 1000.0, eps: float = 1e-05)[source]

Bases: object

The expression builder allows to convert logical expression into mixed integer constraints. In the process it also creates all necessary auxiliary variables. The structure of of interface is as follows:

Create expression builder instance.

Generate expressions. Constraints and an output variable are created (or an existing output variable referenced) for each expression. The corresponding ModelElements are internally stored in self.model_elements.

Obtain all generated ModelElements from self.model_elements.

The MIP conversions here are based on

@article{brown2007formulating,: title={Formulating integer linear programs: A rogues’ gallery}, author={Brown, Gerald G and Dell, Robert F}, journal={INFORMS Transactions on Education}, volume={7}, number={2}, pages={153–159}, year={2007}, publisher={INFORMS}

}

IMPORTANT NOTE: The Integrality Tolerance of the used solver has to be set such that IntFeasTol * M < eps for all the constraints to work correctly.

Parameters:

entity (ModelEntity) – Entity used to obtain referenced pyomo model elements from.
M (int, optional) – Constant for bigM constraints. Defaults to 1e3.
eps (float, optional) – Slack value for strict inequalities (pyomo only allows for <=, >=, ==). Defaults to 1e-5.

Methods

`enforce_value`	Generates an always-true constraint for a: val == a
`from_and`	Generates constraints based on: out = 1 if (a and b), out = 0 otherwise.
`from_geq`	Generates constraints based on: out = 1 if a >= b, out = 0 otherwise.
`from_gt`	Generates constraints based on: out = 1 if a > b, out = 0 otherwise.
`from_not`	Generates a constraint based on: out = 1 - a The MILP formulation is: out == 1 - a
`from_or`	Generates constraints based on: out = 1 if (a or b), out = 0 otherwise.

Helper method to access elements from self.entity’s pyomo model. Enforces that the variable is expanded for robustness.

Parameters:

scenario (ConstraintScenario) – Scenario to access.
var (Union[str, int, float, list[int], list[float]]) – Either variable name or constant value.
model (ConcreteModel) – Pyomo model to access.
t (int) – Time index.

Returns:

Union[Union[Var, Param], int, float] – Either pyomo element or constant value.

Helper method to access elements from self.entity’s pyomo model.

Parameters:

scenario (ConstraintScenario) – Scenario to access.
var (Union[str, int, float, list[int], list[float]]) – Either variable name or constant value.
model (ConcreteModel) – Pyomo model to access.
t (int) – Time index.
expand_variable (bool, optional) – Tells the scenario that this variable should be expanded for robustness. Defaults to False.

Returns:

Union[Union[Var, Param], int, float] – Either pyomo element or constant value.

enforce_value(a: str, val: int | float) → None[source]

Generates an always-true constraint for a: val == a

Parameters:

a (str) – Variable 1.
val (Union[int, float]) – value the variable should be set to.

from_and(a: str, b: str, out: str | None = None, is_new: bool = True) → str[source]

Generates constraints based on: out = 1 if (a and b), out = 0 otherwise. The MILP formulation is: out >= a + b - 1 out <= a out <= b

Parameters:

a (str) – Variable 1 (must be binary).
b (str) – Variable 2 (must be binary).
out (str, optional) – Name of the output variable. If not given, a name is autogenerated.
is_new (bool, optional) – Indicates if the variable is new. If so, a corresponding ModelElement added. Defaults to True.
given (If not)
added. (a name is autogenerated and a corresponding ModelElement)

Returns:

str – Name of the output variable.

Generates constraints based on: out = 1 if a >= b, out = 0 otherwise. The MILP formulation using bigM constraints is: a >= b - M*(1-out) a < b + M*out (we use: a + eps <= b + M*out)

Parameters:

a (Union[str, int, float]) – Left hand side of the inequality.
b (Union[str, int, float]) – Right hand side of the inequality.
out (str, optional) – Name of the output variable. If not given, a name is autogenerated (’aux_’ + 5 hex characters).
is_new (bool, optional) – Indicates if the variable is new. If so, a corresponding ModelElement added. Defaults to True.
M (int, optional) – Constant M for bigM type constraints. If not given, the class’ M is used.

Returns:

str – Name of the output variable

Generates constraints based on: out = 1 if a > b, out = 0 otherwise. The MILP formulation using bigM constraints is: a - eps >= b - M*(1-out) a <= b + M*out

Parameters:

a (Union[str, int, float]) – Left hand side of the inequality.
b (Union[str, int, float]) – Right hand side of the inequality.
out (str, optional) – Name of the output variable. If not given, a name is autogenerated.
is_new (bool, optional) – Indicates if the variable is new. If so, a corresponding ModelElement added. Defaults to True.
M (int, optional) – Constant M for bigM type constraints. If not given, the class’ M is used.

Returns:

str – Name of the output variable

from_not(a: str, out: str | None = None, is_new: bool = True) → str[source]

Generates a constraint based on: out = 1 - a The MILP formulation is: out == 1 - a

Parameters:

a (str) – Variable 1 (must be binary)
out (str, optional) – Name of the output variable. If not given, a name is autogenerated.
is_new (bool, optional) – Indicates if the variable is new. If so, a corresponding ModelElement added. Defaults to True.
given (If not)
added. (a name is autogenerated and a corresponding ModelElement)

Returns:

str – Name of the output variable.

from_or(a: str, b: str, out: str | None = None, is_new: bool = True) → str[source]

Generates constraints based on: out = 1 if (a or b), out = 0 otherwise. The MILP formulation is: out <= a + b out >= a out >= b

Parameters:

a (str) – Variable 1 (must be binary).
b (str) – Variable 2 (must be binary).
out (str, optional) – Name of the output variable. If not given, a name is autogenerated.
is_new (bool, optional) – Indicates if the variable is new. If so, a corresponding ModelElement added. Defaults to True.
given (If not)
added. (a name is autogenerated and a corresponding ModelElement)

Returns:

str – Name of the output variable.