from __future__ import annotations
from typing import Optional
from typing import TYPE_CHECKING
import numpy as np
from optuna._experimental import experimental_class
from optuna.samplers.nsgaii._crossovers._base import BaseCrossover
if TYPE_CHECKING:
from optuna.study import Study
[docs]
@experimental_class("3.0.0")
class SBXCrossover(BaseCrossover):
"""Simulated Binary Crossover operation used by :class:`~optuna.samplers.NSGAIISampler`.
Generates a child from two parent individuals
according to the polynomial probability distribution.
- `Deb, K. and R. Agrawal.
“Simulated Binary Crossover for Continuous Search Space.”
Complex Syst. 9 (1995): n. pag.
<https://www.complex-systems.com/abstracts/v09_i02_a02/>`_
Args:
eta:
Distribution index. A small value of ``eta`` allows distant solutions
to be selected as children solutions. If not specified, takes default
value of ``2`` for single objective functions and ``20`` for multi objective.
"""
n_parents = 2
def __init__(self, eta: Optional[float] = None) -> None:
self._eta = eta
[docs]
def crossover(
self,
parents_params: np.ndarray,
rng: np.random.RandomState,
study: Study,
search_space_bounds: np.ndarray,
) -> np.ndarray:
# https://www.researchgate.net/profile/M-M-Raghuwanshi/publication/267198495_Simulated_Binary_Crossover_with_Lognormal_Distribution/links/5576c78408ae7536375205d7/Simulated-Binary-Crossover-with-Lognormal-Distribution.pdf
# Section 2 Simulated Binary Crossover (SBX)
# To avoid generating solutions that violate the box constraints,
# alpha1, alpha2, xls and xus are introduced, unlike the reference.
xls = search_space_bounds[..., 0]
xus = search_space_bounds[..., 1]
xs_min = np.min(parents_params, axis=0)
xs_max = np.max(parents_params, axis=0)
if self._eta is None:
eta = 20.0 if study._is_multi_objective() else 2.0
else:
eta = self._eta
xs_diff = np.clip(xs_max - xs_min, 1e-10, None)
beta1 = 1 + 2 * (xs_min - xls) / xs_diff
beta2 = 1 + 2 * (xus - xs_max) / xs_diff
alpha1 = 2 - np.power(beta1, -(eta + 1))
alpha2 = 2 - np.power(beta2, -(eta + 1))
us = rng.rand(len(search_space_bounds))
mask1 = us > 1 / alpha1 # Equation (3).
betaq1 = np.power(us * alpha1, 1 / (eta + 1)) # Equation (3).
betaq1[mask1] = np.power((1 / (2 - us * alpha1)), 1 / (eta + 1))[mask1] # Equation (3).
mask2 = us > 1 / alpha2 # Equation (3).
betaq2 = np.power(us * alpha2, 1 / (eta + 1)) # Equation (3)
betaq2[mask2] = np.power((1 / (2 - us * alpha2)), 1 / (eta + 1))[mask2] # Equation (3).
c1 = 0.5 * ((xs_min + xs_max) - betaq1 * xs_diff) # Equation (4).
c2 = 0.5 * ((xs_min + xs_max) + betaq2 * xs_diff) # Equation (5).
# SBX applies crossover with establishment 0.5, and with probability 0.5,
# the gene of the parent individual is the gene of the child individual.
# The original SBX creates two child individuals,
# but optuna's implementation creates only one child individual.
# Therefore, when there is no crossover,
# the gene is selected with equal probability from the parent individuals x1 and x2.
child_params_list = []
for c1_i, c2_i, x1_i, x2_i in zip(c1, c2, parents_params[0], parents_params[1]):
if rng.rand() < 0.5:
if rng.rand() < 0.5:
child_params_list.append(c1_i)
else:
child_params_list.append(c2_i)
else:
if rng.rand() < 0.5:
child_params_list.append(x1_i)
else:
child_params_list.append(x2_i)
child_params = np.array(child_params_list)
return child_params