import numpy as np
from abc import abstractmethod
from typing import Union
[docs]class GLIDEError(Exception):
"""Raised when an error related to the ASF classes is encountered.
"""
[docs]class GLIDEBase:
"""
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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
self.has_additional_constraints = False
self.utopian = utopian
self.nadir = nadir
self.rho = rho
self.required_keys: dict = {}
self.extras = kwargs
[docs] def __call__(self, objective_vector: np.ndarray, preference: dict) -> np.ndarray:
"""Evaluate the scalarization function value based on objective vectors and
DM preference.
Args:
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:
np.ndarray: The scalarized value obtained by using GLIDE-II over
objective_vector.
"""
self.preference = preference
self.objective_vector = np.atleast_2d(objective_vector)
f_minus_q = self.objective_vector - self.q
mu = np.atleast_2d(self.mu)
I_alpha = self.I_alpha
max_term = np.max(mu[:, I_alpha] * f_minus_q[:, I_alpha], axis=1)
sum_term = self.rho * np.sum(self.w * f_minus_q, axis=1)
return max_term + sum_term
[docs] def evaluate_constraints(
self, objective_vector: np.ndarray, preference: dict
) -> Union[None, np.ndarray]:
# TODO: Description for Args & Returns are yet to be filled.
"""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.
Args:
objective_vector (np.ndarray): [description]
preference (dict): [description]
Returns:
Union[None, np.ndarray]: [description]
"""
if not self.has_additional_constraints:
return None
self.preference = preference
self.objective_vector = np.atleast_2d(objective_vector)
constraints = (
self.epsilon[self.I_epsilon]
+ self.s_epsilon * self.delta_epsilon[self.I_epsilon]
- self.objective_vector[:, self.I_epsilon]
)
return constraints
@property
@abstractmethod
[docs] def I_alpha(self):
pass
@property
@abstractmethod
[docs] def I_epsilon(self):
pass
@property
@abstractmethod
@property
@abstractmethod
@property
@abstractmethod
@property
@abstractmethod
[docs] def epsilon(self):
pass
@property
@abstractmethod
[docs] def s_epsilon(self):
pass
@property
@abstractmethod
[docs] def delta_epsilon(self):
pass
[docs]class reference_point_method_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=nadir, rho=rho, **kwargs)
self.has_additional_constraints = False
self.__I_alpha = np.full_like(
utopian, dtype=np.bool_, fill_value=True
).flatten()
self.__I_epsilon = np.full_like(
utopian, dtype=np.bool_, fill_value=False
).flatten()
self.__w = 1
self.__mu = 1 / (nadir - utopian)
self.required_keys = {
"reference point": (
"Used to calculate the direction of improvement: "
"a line parallel to the nadir-utopian vector "
"and passing through the reference point. "
"(type: numpy.ndarray)"
)
}
@property
[docs] def I_epsilon(self):
return self.__I_epsilon
@property
[docs] def I_alpha(self):
return self.__I_alpha
@property
[docs] def mu(self):
return self.__mu
@property
[docs] def w(self):
return self.__w
@property
[docs] def q(self):
return self.preference["reference point"]
@property
[docs] def epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def s_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def delta_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
[docs]class GUESS_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=nadir, rho=rho, **kwargs)
self.has_additional_constraints = False
self.__I_alpha = np.full_like(
utopian, dtype=np.bool_, fill_value=True
).flatten()
self.__I_epsilon = np.full_like(
utopian, dtype=np.bool_, fill_value=False
).flatten()
self.__w = 0
self.required_keys = {
"reference point": (
"Used to calculate the direction of improvement: "
"a line going from the nadir point to the reference point. "
"(type: numpy.ndarray)"
)
}
@property
[docs] def I_epsilon(self):
return self.__I_epsilon
@property
[docs] def I_alpha(self):
return self.__I_alpha
@property
[docs] def mu(self):
return 1 / (self.nadir - self.preference["reference point"])
@property
[docs] def w(self):
return self.__w
@property
[docs] def q(self):
return self.preference["reference point"]
@property
[docs] def epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def s_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def delta_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
[docs]class AUG_GUESS_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=nadir, rho=rho, **kwargs)
self.__w = 1
[docs]class NIMBUS_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=nadir, rho=rho, **kwargs)
self.__mu = self.__w = 1 / (self.nadir - self.utopian)
self.has_additional_constraints = True
self.required_keys = {
"current solution": (
"A solution preferred by the DM currently. " "(type: numpy.ndarray)"
),
"classifications": (
"A list of same length as the number of objectives. Elements can only "
"include some or all of ['<', '<=', '=', '>=', '0']. These classify "
"the different objectives as defined in the NIMBUS or GLIDE-II paper. "
"(type: list)"
),
"levels": (
"A vector containing desirable levels of objectives or constraining bounds "
"depending on the classification. Same length as the number of objectives. "
"(type: numpy.ndarray)"
),
}
@property
[docs] def improve_unconstrained(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == "<")[0]
indices[relevant] = True
return indices
@property
[docs] def improve_constrained(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == "<=")[0]
indices[relevant] = True
return indices
@property
[docs] def satisfactory(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == "=")[0]
indices[relevant] = True
return indices
@property
[docs] def relax_constrained(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == ">=")[0]
indices[relevant] = True
return indices
@property
[docs] def relax_unconstrained(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == "0")[0]
indices[relevant] = True
return indices
@property
[docs] def I_alpha(self):
return self.improve_unconstrained + self.improve_constrained
@property
[docs] def I_epsilon(self):
return (
self.improve_unconstrained
+ self.improve_constrained
+ self.satisfactory
+ self.relax_constrained
)
@property
[docs] def w(self):
# This was in the paper
return self.__w
# This is what I think it should be. There may be division by zero errors here.
"""return (self.objective_vector / (self.objective_vector - self.q)) / (
self.nadir - self.utopian
)"""
@property
[docs] def mu(self):
return self.__mu
@property
[docs] def q(self):
q = np.full_like(self.utopian, fill_value=0, dtype=float)
q[self.improve_unconstrained] = self.utopian[self.improve_unconstrained]
q[self.improve_constrained] = self.preference["levels"][
self.improve_constrained
]
return q
@property
[docs] def epsilon(self):
e = np.full_like(self.utopian, fill_value=np.nan, dtype=float)
case1 = (
self.improve_constrained + self.improve_unconstrained + self.satisfactory
)
case2 = self.relax_constrained
e[case1] = self.preference["current solution"][case1]
e[case2] = self.preference["levels"][case2]
return e
@property
[docs] def s_epsilon(self):
return 0
@property
[docs] def delta_epsilon(self):
return np.zeros_like(self.utopian)
[docs]class STEP_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=nadir, rho=rho, **kwargs)
self.__mu = (self.nadir - self.utopian) / np.max(
np.abs(np.vstack((utopian, nadir))), axis=0
)
self.__w = 0
self.I_epsilon = np.full_like(self.utopian, dtype=np.bool_, fill_value=True)
self.has_additional_constraints = True
self.required_keys = {
"current solution": (
"A solution preferred by the DM currently. " "(type: numpy.ndarray)"
),
"classifications": (
"A list of same length as the number of objectives. Elements can only "
"include some or all of [<=', '=', '>=']. These classify "
"the different objectives as defined in the GLIDE-II paper. "
"(type: list)"
),
"levels": (
"A vector containing desirable levels of objectives or constraining bounds "
"depending on the classification. Same length as the number of objectives. "
"(type: numpy.ndarray)"
),
}
@property
[docs] def improve_constrained(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == "<=")[0]
indices[relevant] = True
return indices
@property
[docs] def satisfactory(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == "=")[0]
indices[relevant] = True
return indices
@property
[docs] def relax_constrained(self):
indices = np.full_like(self.utopian, dtype=np.bool_, fill_value=False)
relevant = np.where(np.array(self.preference["classifications"]) == ">=")[0]
indices[relevant] = True
return indices
@property
[docs] def I_alpha(self):
return self.improve_constrained
@property
[docs] def w(self):
# This was in the paper
return self.__w
@property
[docs] def mu(self):
return self.__mu
@property
[docs] def q(self):
q = np.full_like(self.utopian, fill_value=0, dtype=float)
q[self.improve_constrained] = self.utopian[self.improve_constrained]
return q
@property
[docs] def epsilon(self):
e = np.full_like(self.utopian, fill_value=np.nan, dtype=float)
case1 = self.improve_constrained + self.satisfactory
case2 = self.relax_constrained
e[case1] = self.preference["current solution"][case1]
e[case2] = self.preference["levels"][case2]
return e
@property
[docs] def s_epsilon(self):
return 0
@property
[docs] def delta_epsilon(self):
return np.zeros_like(self.utopian)
[docs]class STOM_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=None, rho=rho, **kwargs)
self.has_additional_constraints = False
self.__I_alpha = np.full_like(
utopian, dtype=np.bool_, fill_value=True
).flatten()
self.__I_epsilon = np.full_like(
utopian, dtype=np.bool_, fill_value=False
).flatten()
self.__w = 0
self.required_keys = {
"reference point": (
"Used to calculate the direction of improvement: "
"a line going from the reference point to the utopian point. "
"(type: numpy.ndarray)"
)
}
@property
[docs] def I_epsilon(self):
return self.__I_epsilon
@property
[docs] def I_alpha(self):
return self.__I_alpha
@property
[docs] def mu(self):
return 1 / (self.preference["reference point"] - self.utopian)
@property
[docs] def w(self):
return self.__w
@property
[docs] def q(self):
return self.utopian
@property
[docs] def epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def s_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def delta_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
[docs]class AUG_STOM_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=None, rho=rho, **kwargs)
self.has_additional_constraints = False
self.__w = 1
[docs]class Tchebycheff_GLIDE(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.
Args:
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.
"""
def __init__(
self,
utopian: np.ndarray = None,
nadir: np.ndarray = None,
rho: float = 1e-6,
**kwargs
):
super().__init__(utopian=utopian, nadir=None, rho=rho, **kwargs)
self.has_additional_constraints = False
self.__I_alpha = np.full_like(
utopian, dtype=np.bool_, fill_value=True
).flatten()
self.__I_epsilon = np.full_like(
utopian, dtype=np.bool_, fill_value=False
).flatten()
self.__w = 1
self.required_keys = {
"mu": (
"Vector defining the direction of improvement of the scalarizer. "
"(type: numpy.ndarray)"
)
}
@property
[docs] def I_epsilon(self):
return self.__I_epsilon
@property
[docs] def I_alpha(self):
return self.__I_alpha
@property
[docs] def mu(self):
return self.preference["mu"]
@property
[docs] def w(self):
return self.__w
@property
[docs] def q(self):
return self.utopian
@property
[docs] def epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def s_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def delta_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
[docs]class PROJECT_GLIDE(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.
Args:
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.
"""
def __init__(
self, current_objective_vector: np.ndarray, rho: float = 1e-6, **kwargs
):
super().__init__(utopian=None, nadir=None, rho=rho, **kwargs)
self.current_objective_vector = current_objective_vector
self.has_additional_constraints = False
self.__I_alpha = np.full_like(
current_objective_vector, dtype=np.bool_, fill_value=True
).flatten()
self.__I_epsilon = np.full_like(
current_objective_vector, dtype=np.bool_, fill_value=False
).flatten()
self.__w = 0
@property
[docs] def I_epsilon(self):
return self.__I_epsilon
@property
[docs] def I_alpha(self):
return self.__I_alpha
@property
[docs] def mu(self):
return 1 / np.abs(
self.preference["reference point"] - self.current_objective_vector
)
@property
[docs] def w(self):
return self.__w
@property
[docs] def q(self):
return self.utopian
@property
[docs] def epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def s_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
@property
[docs] def delta_epsilon(self):
msg = "This part of the code should not be reached. Contact maintaner."
raise GLIDEError(msg)
