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"""Class for indicator contraints (IndicatorConstraints)"""
[docs]class IndicatorConstraints:
"""A class for storing indicator contraints
This class is a container for indicator constraints. Indicator constraints are used to link the fulfillment
of a constraint to an indicating variable. For instance the indicator constraint:
z = 1 -> 2*d - 1*e <= 3
can be described as:
If z=1, then 2*d - 1*e <= 3
An alternative formulation of this association is possible with a bigM constraint:
2*d - 1*e - z*M <= 3, with M = very large
The constraint z = 0 -> 2*d - 1*e <= 3 would translate to 2*d - 1*e + z*M <= 3 + M
Generally, indicator constraints are preferred over bigM, because they provide better numerical stability.
However, not all solvers support indicator constraints
Indicator constraints have the form:
x_binv = indicval -> a * x <sense> b
e.g.,: x_35 = 1 -> 2 * x_2 + 3 *x_3 'L' 6
(<=)
This class contains a set of indicator constraints:
x_binv_1 = indicval_1 -> A_1 * x <sense_1> b_1
x_binv_2 = indicval_2 -> A_2 * x <sense_2> b_2
...
Example:
ic = IndicatorConstraints(binv, A, b, sense, indicval)
Args:
binv (list of int): (e.g.: [25, 27, 30])
The index of the binary, indicating variables (indicators) for all indicator constraints.
Integers are allowed ot occur more than once.
A (sparse.csr_matrix):
Coefficient vectors for all indicator constraints, stored in one matrix, whereas
each row is used in one indicator constraint.
(num_columns = number of variables, num_rows = number of indicator constraints)
b (list of float):
Right hand sides of all indicator constraints. (e.g.: [0.1, 2.0, 3])
sense (str):
(In)equality signs for all indicator constraints.
'L'ess or equal, 'E'qual or, 'G'reater or equal (e.g.: 'EEGLGLGE')
indicval (list of int):
Indicator values for all indicator constraints. Which value of the indicator
enforces the constraint, 0 or 1? (e.g., 0001010110)
Returns:
(IndicatorConstraints):
An object of the IndicatorConstraints class to pass indicator constraints.
"""
def __init__(self, binv, A, b, sense, indicval):
self.binv = binv # index of binary variable
self.A = A # CPLEX: lin_expr, left hand side coefficient row for indicator constraint
self.b = b # right hand side for indicator constraint
self.sense = sense # sense of the indicator constraint can be 'L', 'E', 'G' (lower-equal, equal, greater-equal)
self.indicval = indicval # value the binary variable takes when constraint is fulfilled