import numpy as np
from numpy.typing import NDArray
from star_pso.population.particle import Particle
from star_pso.benchmarks.test_function import TestFunction
from star_pso.utils.auxiliary import identify_global_optima
[docs]
class Shubert(TestFunction):
"""
This function was originally proposed in:
- Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs.
New York: Springer-Verlag, New York, 1996.
"""
def __init__(self, n_dim: int = 2, x_min: float = -10.0, x_max: float = 10.0) -> None:
"""
Default initializer of the Shubert D class.
:param n_dim: (int) the number of dimension of the input space.
:param x_min: (float) the lower bound values of the search space.
:param x_max: (float) the upper bound values of the search space.
:return: None.
"""
# Ensure correct type.
n_dim = int(n_dim)
# Sanity check.
if n_dim < 2:
raise ValueError("Shubert needs at least 2 dimensions.")
# Call the super initializer.
super().__init__(name=f"Shubert_{n_dim}D",
n_dim=n_dim, x_min=x_min, x_max=x_max)
# _end_def_
[docs]
def func(self, x_pos: NDArray) -> NDArray:
"""
This is a multidimensional function with 'n_dim * 3^n_dim'
global optimal values.
:param x_pos: the current position(s) of the function.
:return: the function value(s).
"""
# Initialize function values to NaN.
f_value = np.full_like(x_pos, np.nan, dtype=float)
# Check the valid function range.
if np.all((self.x_min <= x_pos) & (x_pos <= self.x_max)):
# Range 1 to 5.
i = np.array([1, 2, 3, 4, 5])
# Get the product of the sums.
f_value = -np.prod(np.sum(i[:, np.newaxis] * np.cos((i[:, np.newaxis] + 1) * x_pos +
i[:, np.newaxis]), axis=0))
# Return the ndarray.
return f_value
# _end_def_
[docs]
def search_for_optima(self, population: list[Particle],
epsilon: float = 1.0e-4) -> tuple[int, int]:
"""
Searches the input population for the global optimum values
of the specific test function, using default (problem specific)
parameters.
:param population: the population to search the global optimum.
:param epsilon: accuracy level of the global optimal solution.
:return: a tuple with the number of global optima found and the
total number that exist.
"""
# Sanity check.
if self.n_dim > 3:
raise ValueError(f"Unknown 'f_opt' for D = {self.n_dim}")
# _end_if_
# Calculate the total global optima along with
# the f_opt for the given number of dimensions.
if self.n_dim == 2:
total_optima, f_opt = 18, 186.7309088
else:
total_optima, f_opt = 81, 2709.093505
# _end_if_
# Get the global optima particles.
found_optima = identify_global_optima(population, epsilon=epsilon,
radius=0.5, f_opt=f_opt)
# Find the number of optima.
num_optima = len(found_optima)
# Return the tuple (number of found, total number)
return num_optima, total_optima
# _end_def_
# _end_class_