:py:mod:`desdeo_emo.utilities.ReferenceVectors` =============================================== .. py:module:: desdeo_emo.utilities.ReferenceVectors Module Contents --------------- Classes ~~~~~~~ .. autoapisummary:: desdeo_emo.utilities.ReferenceVectors.ReferenceVectors Functions ~~~~~~~~~ .. autoapisummary:: desdeo_emo.utilities.ReferenceVectors.normalize desdeo_emo.utilities.ReferenceVectors.shear desdeo_emo.utilities.ReferenceVectors.rotate desdeo_emo.utilities.ReferenceVectors.householder desdeo_emo.utilities.ReferenceVectors.rotate_toward .. py:function:: normalize(vectors) Normalize a set of vectors. The length of the returned vectors will be unity. :param vectors: Set of vectors of any length, except zero. :type vectors: np.ndarray .. py:function:: shear(vectors, degrees: float = 5) Shear a set of vectors lying on the plane z=0 towards the z-axis, such that the resulting vectors 'degrees' angle away from the z axis. z is the last element of the vector, and has to be equal to zero. :param vectors: The final element of each vector should be zero. :type vectors: numpy.ndarray :param degrees: The angle that the resultant vectors make with the z axis. Unit is radians. (the default is 5) :type degrees: float, optional .. py:function:: rotate(initial_vector, rotated_vector, other_vectors) Calculate the rotation matrix that rotates the initial_vector to the rotated_vector. Apply that rotation on other_vectors and return. Uses Householder reflections twice to achieve this. .. py:function:: householder(vector) Return reflection matrix via householder transformation. .. py:function:: rotate_toward(initial_vector, final_vector, other_vectors, degrees: float = 5) Rotate other_vectors (with the centre at initial_vector) towards final_vector by an angle degrees. :param initial_vector: Centre of the vectors to be rotated. :type initial_vector: np.ndarray :param final_vector: The final position of the center of other_vectors. :type final_vector: np.ndarray :param other_vectors: The array of vectors to be rotated :type other_vectors: np.ndarray :param degrees: The amount of rotation (the default is 5) :type degrees: float, optional :returns: * **rotated_vectors** (*np.ndarray*) -- The rotated vectors * **reached** (*bool*) -- True if final_vector has been reached .. py:class:: ReferenceVectors(lattice_resolution: int = None, number_of_vectors: int = None, number_of_objectives: int = None, creation_type: str = 'Uniform', vector_type: str = 'Spherical', ref_point: list = None) Class object for reference vectors. .. py:method:: _create(creation_type: str = 'Uniform') Create the reference vectors. :param creation_type: 'Uniform' creates the reference vectors uniformly using simplex lattice design. 'Focused' creates reference vectors symmetrically around a central reference vector. By default 'Uniform'. :type creation_type: str, optional .. py:method:: normalize() Normalize the reference vectors to a unit hypersphere. .. py:method:: neighbouring_angles() -> numpy.ndarray Calculate neighbouring angles for normalization. .. py:method:: adapt(fitness: numpy.ndarray) Adapt reference vectors. Then normalize. :param fitness: :type fitness: np.ndarray .. py:method:: interactive_adapt_1(z: numpy.ndarray, n_solutions: int, translation_param: float = 0.2) -> None Adapt reference vectors using the information about prefererred solution(s) selected by the Decision maker. :param z: Preferred solution(s). :type z: np.ndarray :param n_solutions: Number of solutions in total. :type n_solutions: int :param translation_param: Parameter determining how close the reference vectors are to the central vector :type translation_param: float :param \*\*v** defined by using the selected solution: :type \*\*v** defined by using the selected solution: s Returns: .. py:method:: interactive_adapt_2(z: numpy.ndarray, n_solutions: int, predefined_distance: float = 0.2) -> None Adapt reference vectors by using the information about non-preferred solution(s) selected by the Decision maker. After the Decision maker has specified non-preferred solution(s), Euclidian distance between normalized solution vector(s) and each of the reference vectors are calculated. Those reference vectors that are **closer** than a predefined distance are either **removed** or **re-positioned** somewhere else. .. note:: At the moment, only the **removal** of reference vectors is supported. Repositioning of the reference vectors is **not** supported. .. note:: In case the Decision maker specifies multiple non-preferred solutions, the reference vector(s) for which the distance to **any** of the non-preferred solutions is less than predefined distance are removed. .. note:: Future developer should implement a way for a user to say: "Remove some percentage of objecive space/reference vectors" rather than giving a predefined distance value. :param z: Non-preferred solution(s). :type z: np.ndarray :param n_solutions: Number of solutions in total. :type n_solutions: int :param predefined_distance: The reference vectors that are closer than this distance are either removed or :type predefined_distance: float :param re-positioned somewhere else.: :param Default value: 0.2 Returns: .. py:method:: iteractive_adapt_3(ref_point, translation_param=0.2) Adapt reference vectors linearly towards a reference point. Then normalize. The details can be found in the following paper: Hakanen, Jussi & Chugh, Tinkle & Sindhya, Karthik & Jin, Yaochu & Miettinen, Kaisa. (2016). Connections of Reference Vectors and Different Types of Preference Information in Interactive Multiobjective Evolutionary Algorithms. :param ref_point: :param translation_param: (Default value = 0.2) .. py:method:: interactive_adapt_4(preferred_ranges: numpy.ndarray) -> None Adapt reference vectors by using the information about the Decision maker's preferred range for each of the objective. Using these ranges, Latin hypercube sampling is applied to generate m number of samples between within these ranges, where m is the number of reference vectors. Normalized vectors constructed of these samples are then set as new reference vectors. :param preferred_ranges: Preferred lower and upper bound for each of the objective function values. :type preferred_ranges: np.ndarray Returns: .. py:method:: slow_interactive_adapt(ref_point) Basically a wrapper around rotate_toward. Slowly rotate ref vectors toward ref_point. Return a boolean value to tell if the ref_point has been reached. :param ref_point: The reference vectors will slowly move towards the ref_point. :type ref_point: list or np.ndarray :returns: True if ref_point has been reached. False otherwise. :rtype: boolean .. py:method:: add_edge_vectors() Add edge vectors to the list of reference vectors. Used to cover the entire orthant when preference information is provided.