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"""Define a general class and implementations of achievement scalarizing functions. """ import abc from abc import abstractmethod from os import path from typing import List, Union import numpy as np class ASFError(Exception): """Raised when an error related to the ASF classes is encountered. """ class ASFBase(abc.ABC): """A base class for representing achievement scalarizing functions. Instances of the implementations of this class should function as function. """ @abstractmethod def __call__( self, objective_vector: np.ndarray, reference_point: np.ndarray ) -> Union[float, np.ndarray]: """Evaluate the ASF. Args: objective_vectors (np.ndarray): The objective vectors to calulate the values. reference_point (np.ndarray): The reference point to calculate the values. Returns: Union[float, np.ndarray]: Either a single ASF value or a vector of values if objective is a 2D array. Note: The reference point may not always necessarely be feasible, but it's dimensions should match that of the objective vector. """ pass class SimpleASF(ASFBase): """Implements a simple order-representing ASF. Args: weights (np.ndarray): A weight vector that holds weights. It's length should match the number of objectives in the underlying MOO problem the achievement problem aims to solve. Attributes: weights (np.ndarray): A weight vector that holds weights. It's length should match the number of objectives in the underlying MOO problem the achievement problem aims to solve. """ def __init__(self, weights: np.ndarray): self.weights = weights def __call__( self, objective_vector: np.ndarray, reference_point: np.ndarray ) -> Union[float, np.ndarray]: """Evaluate the simple order-representing ASF. Args: objective_vector (np.ndarray): A vector representing a solution in the solution space. reference_point (np.ndarray): A vector representing a reference point in the solution space. Raises: ASFError: The dimensions of the objective vector and reference point don't match. Note: The shaped of objective_vector and reference_point must match. """ if not objective_vector.shape == reference_point.shape: msg = ( "The dimensions of the objective vector {} and " "reference_point {} do not match." ).format(objective_vector, reference_point) raise ASFError(msg) return np.max( np.where( np.isnan(reference_point), -np.inf, self.weights * (objective_vector - reference_point), ) ) class ReferencePointASF(ASFBase): """Uses a reference point q and preferenial factors to scalarize a MOO problem. Defined in `Miettinen 2010`_ equation (2). Args: preferential_factors (np.ndarray): The preferential factors. nadir (np.ndarray): The nadir point of the MOO problem to be scalarized. utopian_point (np.ndarray): The utopian point of the MOO problem to be scalarized. rho (float): A small number to be used to scale the sm factor in the ASF. Defaults to 0.1. Attributes: preferential_factors (np.ndarray): The preferential factors. nadir (np.ndarray): The nadir point of the MOO problem to be scalarized. utopian_point (np.ndarray): The utopian point of the MOO problem to be scalarized. rho (float): A small number to be used to scale the sm factor in the ASF. Defaults to 0.1. .. _Miettinen 2010: Miettinen, K.; Eskelinen, P.; Ruiz, F. & Luque, M. NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point Europen Joural of Operational Research, 2010, 206, 426-434 """ def __init__( self, preferential_factors: np.ndarray, nadir: np.ndarray, utopian_point: np.ndarray, rho: float = 0.1, ): self.preferential_factors = preferential_factors self.nadir = nadir self.utopian_point = utopian_point self.rho = rho def __call__( self, objective_vector: np.ndarray, reference_point: np.ndarray ) -> Union[float, np.ndarray]: mu = self.preferential_factors f = objective_vector q = reference_point rho = self.rho z_nad = self.nadir z_uto = self.utopian_point max_term = np.max(mu * (f - q), axis=-1) sum_term = rho * np.sum((f - q) / (z_nad - z_uto), axis=-1) return max_term + sum_term class MaxOfTwoASF(ASFBase): """Implements the ASF as defined in eq. 3.1 `Miettinen 2006`_ Args: nadir (np.ndarray): The nadir point. ideal (np.ndarray): The ideal point. lt_inds (List[int]): Indices of the objectives categorized to be decreased. lte_inds (List[int]): Indices of the objectives categorized to be reduced until some value is reached. rho (float): A small number to form the utopian point. rho_sum (float): A small number to be used as a weight for the sum term. Attributes: nadir (np.ndarray): The nadir point. ideal (np.ndarray): The ideal point. lt_inds (List[int]): Indices of the objectives categorized to be decreased. lte_inds (List[int]): Indices of the objectives categorized to be reduced until some value is reached. rho (float): A small number to form the utopian point. rho_sum (float): A small number to be used as a weight for the sum term. .. _Miettinen 2006: Miettinen, K. & Mäkelä, Marko M. Synchronous approach in interactive multiobjective optimization European Journal of Operational Research, 2006, 170, 909-922 """ def __init__( self, nadir: np.ndarray, ideal: np.ndarray, lt_inds: List[int], lte_inds: List[int], rho: float = 1e-6, rho_sum: float = 1e-6, ): self.nadir = nadir self.ideal = ideal self.lt_inds = lt_inds self.lte_inds = lte_inds self.rho = rho self.rho_sum = rho_sum def __call__( self, objective_vector: np.ndarray, reference_point: np.ndarray ) -> Union[float, np.ndarray]: # assure this function works with single objective vectors if objective_vector.ndim == 1: f = objective_vector.reshape((1, -1)) else: f = objective_vector ii = self.lt_inds jj = self.lte_inds z = reference_point nad = self.nadir ide = self.ideal uto = self.ideal - self.rho lt_term = (f[:, ii] - ide[ii]) / (nad[ii] - uto[ii]) lte_term = (f[:, jj] - z[jj]) / (nad[jj] - uto[jj]) max_term = np.max(np.hstack((lt_term, lte_term)), axis=1) sum_term = self.rho_sum * np.sum(f / (nad - uto), axis=1) return max_term + sum_term class StomASF(ASFBase): """Implementation of the satisficing trade-off method (STOM) as presented in `Miettinen 2006` equation (3.2) Args: ideal (np.ndarray): The ideal point. rho (float): A small number to form the utopian point. rho_sum (float): A small number to be used as a weight for the sum term. Attributes: ideal (np.ndarray): The ideal point. rho (float): A small number to form the utopian point. rho_sum (float): A small number to be used as a weight for the sum term. .. _Miettinen 2006: Miettinen, K. & Mäkelä, Marko M.