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 UnevenDecreasingMaxima(TestFunction):
"""
This function was originally proposed in:
- K. Deb, “Genetic algorithms in multimodal function optimization
(master thesis and tcga report no. 89002)”, Ph.D. dissertation,
Tuscaloosa: University of Alabama, The Clearinghouse for Genetic
Algorithms, 1989.
"""
def __init__(self, x_min: float = 0.0, x_max: float = 1.0) -> None:
"""
Default initializer of the UnevenDecreasingMaxima class.
: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.
"""
# Call the super initializer.
super().__init__(name="Uneven_Decreasing_Maxima",
n_dim=1, x_min=x_min, x_max=x_max)
# _end_def_
[docs]
def func(self, x_pos: NDArray) -> NDArray:
"""
This is 1D function. There is 1 global and 4 local optima.
: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)
# Condition for the valid range.
if np.all((self.x_min <= x_pos) & (x_pos <= self.x_max)):
f_value = (np.exp(-2.0 * np.log(2.0) * ((x_pos - 0.08)/0.854)**2) *
np.sin(5.0 * np.pi * (x_pos**(3/4) - 0.05))**6)
# Return the value.
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.
"""
# Get the global optima particles.
found_optima = identify_global_optima(population, epsilon=epsilon,
radius=0.01, f_opt=1.0)
# Find the number of optima.
num_optima = len(found_optima)
# Return the tuple (number of found, total number)
return num_optima, 1
# _end_def_
# _end_class_