Source code for optuna.samplers.nsgaii._crossovers._undx

from typing import Optional

import numpy as np

from optuna._experimental import experimental_class
from optuna.samplers.nsgaii._crossovers._base import BaseCrossover
from optuna.study import Study


[docs] @experimental_class("3.0.0") class UNDXCrossover(BaseCrossover): """Unimodal Normal Distribution Crossover used by :class:`~optuna.samplers.NSGAIISampler`. Generates child individuals from the three parents using a multivariate normal distribution. - `H. Kita, I. Ono and S. Kobayashi, Multi-parental extension of the unimodal normal distribution crossover for real-coded genetic algorithms, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), 1999, pp. 1581-1588 Vol. 2 <https://ieeexplore.ieee.org/document/782672>`_ Args: sigma_xi: Parametrizes normal distribution from which ``xi`` is drawn. sigma_eta: Parametrizes normal distribution from which ``etas`` are drawn. If not specified, defaults to ``0.35 / sqrt(len(search_space))``. """ n_parents = 3 def __init__(self, sigma_xi: float = 0.5, sigma_eta: Optional[float] = None) -> None: self._sigma_xi = sigma_xi self._sigma_eta = sigma_eta def _distance_from_x_to_psl(self, parents_params: np.ndarray) -> np.floating: # The line connecting x1 to x2 is called psl (primary search line). # Compute the 2-norm of the vector orthogonal to psl from x3. e_12 = UNDXCrossover._normalized_x1_to_x2( parents_params ) # Normalized vector from x1 to x2. v_13 = parents_params[2] - parents_params[0] # Vector from x1 to x3. v_12_3 = v_13 - np.dot(v_13, e_12) * e_12 # Vector orthogonal to v_12 through x3. m_12_3 = np.linalg.norm(v_12_3, ord=2) # 2-norm of v_12_3. return m_12_3 def _orthonormal_basis_vector_to_psl(self, parents_params: np.ndarray, n: int) -> np.ndarray: # Compute orthogonal basis vectors for the subspace orthogonal to psl. e_12 = UNDXCrossover._normalized_x1_to_x2( parents_params ) # Normalized vector from x1 to x2. basis_matrix = np.identity(n) if np.count_nonzero(e_12) != 0: basis_matrix[0] = e_12 basis_matrix_t = basis_matrix.T Q, _ = np.linalg.qr(basis_matrix_t) return Q.T[1:]
[docs] def crossover( self, parents_params: np.ndarray, rng: np.random.RandomState, study: Study, search_space_bounds: np.ndarray, ) -> np.ndarray: # https://ieeexplore.ieee.org/document/782672 # Section 2 Unimodal Normal Distribution Crossover n = len(search_space_bounds) xp = (parents_params[0] + parents_params[1]) / 2 # Section 2 (2). d = parents_params[0] - parents_params[1] # Section 2 (3). if self._sigma_eta is None: sigma_eta = 0.35 / np.sqrt(n) else: sigma_eta = self._sigma_eta etas = rng.normal(0, sigma_eta**2, size=n) xi = rng.normal(0, self._sigma_xi**2) es = self._orthonormal_basis_vector_to_psl( parents_params, n ) # Orthonormal basis vectors of the subspace orthogonal to the psl. one = xp # Section 2 (5). two = xi * d # Section 2 (5). if n > 1: # When n=1, there is no subsearch component. three = np.zeros(n) # Section 2 (5). D = self._distance_from_x_to_psl(parents_params) # Section 2 (4). for i in range(n - 1): three += etas[i] * es[i] three *= D child_params = one + two + three else: child_params = one + two return child_params
@staticmethod def _normalized_x1_to_x2(parents_params: np.ndarray) -> np.ndarray: # Compute the normalized vector from x1 to x2. v_12 = parents_params[1] - parents_params[0] m_12 = np.linalg.norm(v_12, ord=2) e_12 = v_12 / np.clip(m_12, 1e-10, None) return e_12