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 SPXCrossover(BaseCrossover):
"""Simplex Crossover operation used by :class:`~optuna.samplers.NSGAIISampler`.
Uniformly samples child individuals from within a single simplex
that is similar to the simplex produced by the parent individual.
For further information about SPX crossover, please refer to the following paper:
- `Shigeyoshi Tsutsui and Shigeyoshi Tsutsui and David E. Goldberg and
David E. Goldberg and Kumara Sastry and Kumara Sastry
Progress Toward Linkage Learning in Real-Coded GAs with Simplex Crossover.
IlliGAL Report. 2000.
<https://www.researchgate.net/publication/2388486_Progress_Toward_Linkage_Learning_in_Real-Coded_GAs_with_Simplex_Crossover>`_
Args:
epsilon:
Expansion rate. If not specified, defaults to ``sqrt(len(search_space) + 2)``.
"""
n_parents = 3
def __init__(self, epsilon: Optional[float] = None) -> None:
self._epsilon = epsilon
[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/publication/2388486_Progress_Toward_Linkage_Learning_in_Real-Coded_GAs_with_Simplex_Crossover
# Section 2 A Brief Review of SPX
n = self.n_parents - 1
G = np.mean(parents_params, axis=0) # Equation (1).
rs = np.power(rng.rand(n), 1 / (np.arange(n) + 1)) # Equation (2).
epsilon = np.sqrt(len(search_space_bounds) + 2) if self._epsilon is None else self._epsilon
xks = [G + epsilon * (pk - G) for pk in parents_params] # Equation (3).
ck = 0 # Equation (4).
for k in range(1, self.n_parents):
ck = rs[k - 1] * (xks[k - 1] - xks[k] + ck)
child_params = xks[-1] + ck # Equation (5).
return child_params