scalarization.GLIDE_II

Module Contents

Classes

GLIDEBase

Implements the non-differentiable variant of GLIDE-II as proposed in

reference_point_method_GLIDE

Implements the reference point method of preference elicitation and scalarization

GUESS_GLIDE

Implements the GUESS method of preference elicitation and scalarization

AUG_GUESS_GLIDE

Implements the Augmented GUESS method of preference elicitation and scalarization

NIMBUS_GLIDE

Implements the NIMBUS method of preference elicitation and scalarization

STEP_GLIDE

Implements the STEP method of preference elicitation and scalarization

STOM_GLIDE

Implements the STOM method of preference elicitation and scalarization

AUG_STOM_GLIDE

Implements the Augmented STOM method of preference elicitation and scalarization

Tchebycheff_GLIDE

Implements the Tchebycheff method of preference elicitation and scalarization

PROJECT_GLIDE

Implements the PROJECT method of preference elicitation and scalarization
exception scalarization.GLIDE_II.GLIDEError[source]

Bases: Exception

Raised when an error related to the ASF classes is encountered.

Initialize self. See help(type(self)) for accurate signature.

class scalarization.GLIDE_II.GLIDEBase(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Implements the non-differentiable variant of GLIDE-II as proposed in Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Note

Additional contraints produced by the GLIDE-II formulation are implemented such that if the returned values are negative, the corresponding constraint is violated. The returned value may be positive. In such cases, the returned value is a measure of how close or far the corresponding feasible solution is from violating the constraint.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

abstract property I_alpha[source]
abstract property I_epsilon[source]
abstract property mu[source]
abstract property q[source]
abstract property w[source]
abstract property epsilon[source]
abstract property s_epsilon[source]
abstract property delta_epsilon[source]
__call__(objective_vector: numpy.ndarray, preference: dict) → numpy.ndarray[source]

Evaluate the scalarization function value based on objective vectors and DM preference.

Parameters:

  • objective_vector (np.ndarray) – 2-dimensional array of objective values of solutions.

  • preference (dict) – The preference given by the decision maker. The required dictionary keys and their meanings can be found in self.required_keys variable.

Returns:

The scalarized value obtained by using GLIDE-II over

objective_vector.

Return type:

np.ndarray

evaluate_constraints(objective_vector: numpy.ndarray, preference: dict) → None | numpy.ndarray[source]

Evaluate the additional contraints generated by the GLIDE-II formulation.

Note

Additional contraints produced by the GLIDE-II formulation are implemented such that if the returned values are negative, the corresponding constraint is violated. The returned value may be positive. In such cases, the returned value is a measure of how close or far the corresponding feasible solution is from violating the constraint.

Parameters:

  • objective_vector (np.ndarray) – [description]

  • preference (dict) – [description]

Returns:

[description]

Return type:

Union[None, np.ndarray]

class scalarization.GLIDE_II.reference_point_method_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: GLIDEBase

Implements the reference point method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

property I_epsilon[source]
property I_alpha[source]
property mu[source]
property w[source]
property q[source]
property epsilon[source]
property s_epsilon[source]
property delta_epsilon[source]
class scalarization.GLIDE_II.GUESS_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: GLIDEBase

Implements the GUESS method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

property I_epsilon[source]
property I_alpha[source]
property mu[source]
property w[source]
property q[source]
property epsilon[source]
property s_epsilon[source]
property delta_epsilon[source]
class scalarization.GLIDE_II.AUG_GUESS_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: GUESS_GLIDE

Implements the Augmented GUESS method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

class scalarization.GLIDE_II.NIMBUS_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: GLIDEBase

Implements the NIMBUS method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

property improve_unconstrained[source]
property improve_constrained[source]
property satisfactory[source]
property relax_constrained[source]
property relax_unconstrained[source]
property I_alpha[source]
property I_epsilon[source]
property w[source]
property mu[source]
property q[source]
property epsilon[source]
property s_epsilon[source]
property delta_epsilon[source]
class scalarization.GLIDE_II.STEP_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: GLIDEBase

Implements the STEP method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

property improve_constrained[source]
property satisfactory[source]
property relax_constrained[source]
property I_alpha[source]
property w[source]
property mu[source]
property q[source]
property epsilon[source]
property s_epsilon[source]
property delta_epsilon[source]
class scalarization.GLIDE_II.STOM_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: GLIDEBase

Implements the STOM method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Has no effect on STOM calculation. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

property I_epsilon[source]
property I_alpha[source]
property mu[source]
property w[source]
property q[source]
property epsilon[source]
property s_epsilon[source]
property delta_epsilon[source]
class scalarization.GLIDE_II.AUG_STOM_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: STOM_GLIDE

Implements the Augmented STOM method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Has no effect on STOM calculation. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

class scalarization.GLIDE_II.Tchebycheff_GLIDE(utopian: numpy.ndarray = None, nadir: numpy.ndarray = None, rho: float = 1e-06, **kwargs)[source]

Bases: GLIDEBase

Implements the Tchebycheff method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

property I_epsilon[source]
property I_alpha[source]
property mu[source]
property w[source]
property q[source]
property epsilon[source]
property s_epsilon[source]
property delta_epsilon[source]
class scalarization.GLIDE_II.PROJECT_GLIDE(current_objective_vector: numpy.ndarray, rho: float = 1e-06, **kwargs)[source]

Bases: GLIDEBase

Implements the PROJECT method of preference elicitation and scalarization using the non-differentiable variant of GLIDE-II as proposed in: Ruiz, Francisco, Mariano Luque, and Kaisa Miettinen. “Improving the computational efficiency in a global formulation (GLIDE) for interactive multiobjective optimization.” Annals of Operations Research 197.1 (2012): 47-70.

Parameters:

  • utopian (np.ndarray, optional) – The utopian point. Defaults to None.

  • nadir (np.ndarray, optional) – The nadir point. Defaults to None.

  • rho (float, optional) – The augmentation term for the scalarization function. Defaults to 1e-6.

property I_epsilon[source]
property I_alpha[source]
property mu[source]
property w[source]
property q[source]
property epsilon[source]
property s_epsilon[source]
property delta_epsilon[source]