ObjectiveFunction Class

It manages the objective functions of the optimization problem. it permits to specify the weights of the objectives in case of multi-objective optimization and the optimization directions. Since the variables can be declared in array form, matrix expressions for the objective functions are supported.

Objective functions declarations

The class provides methods to declare variables:

• add_objective_function(objective_function: Expr, minimization: bool = True, weight: float = 1)add an objective function to the optimization problem.

  • objective_function is an expression of the variables of the optimization problem.

  • minimization parameter specifies if the objective function is to be minimized or maximized (optimization direction).

  • weight parameter is the weight of the objective function in case of multi-objective optimization.

Example:

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

variables = Variables()
constraint = Constraints()
a0 = variables.add_binary_variable("a")
b0 = variables.add_discrete_variable("b", [-1, 1, 3])
c0 = variables.add_continuous_variable("c", -2, 2, 0.25, "", "")
objective_function = ObjectiveFunction()
objective_function.add_objective_function(a0 + b0 * c0 + c0**2)