Constraints Class

It manages the constraints of the problem. It is used to store the constraints and to check if a solution satisfies them.

Constraints types supported

Types of constraints supported:

  • Equality, writing the equality as a quadratic penalty function, i.e. sum = b imposed with g = (sum-b)^2

  • Inequality, moving to equality with the continuous auxiliary variables a to be expanded with the encoding technique of the Variables class

  • Not constraint among binary variables, i.e. Not(a) = b imposed with g = 2ab - a - b + 1

  • And constraint among binary variables, i.e. a and b = c imposed with ab -2(a+b)c + 3c

  • Or constraint among binary variables, i.e. a or b = c imposed with ab + (a+b)(1-2c) + c

  • Xor constraint among binary variables, i.e. a xor b = c imposed with 2ab - 2(a+b)c - 4(a+b)_aux+4_aux c +a+b+c+4+_aux

Constraints declarations

The class provides methods to declare variables:

  • add_constraint(expression: str, hard: bool = True, variable_precision: bool = True): adds a constraint to the list of constraints.

    • expression is a string that represents the constraint

    • hard parameter is a boolean that indicates if the constraint is hard or soft.

    • variable_precision parameter is a boolean that indicates if the constraint is to be considered in the precision of the variables.

Example:

from mqt.qao.constraints import Constraints
from mqt.qao.variables import Variables

constraint = Constraints()
variables = Variables()
variables.add_binary_variable("a")
variables.add_binary_variable("b")
variables.add_binary_variable("c")
variables.add_discrete_variable("d", [-1, 1, 3])
variables.add_continuous_variable("e", -2, 2, 0.25, "", "")
constraint.add_constraint("~a = b", True, True, False)
constraint.add_constraint("a | b = c", True, True, False)
constraint.add_constraint("d + e <= 1", True, True, False)