Source code for niapy.benchmarks.cosine_mixture
# encoding=utf8
"""Implementations of Cosine mixture functions."""
import numpy as np
from niapy.benchmarks.benchmark import Benchmark
__all__ = ['CosineMixture']
[docs]class CosineMixture(Benchmark):
r"""Implementations of Cosine mixture function.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Cosine Mixture Function**
:math:`f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-1, 1]`, for all :math:`i = 1, 2,..., D`.
**Global maximum:**
:math:`f(x^*) = -0.1 D`, at :math:`x^* = (0.0,...,0.0)`
LaTeX formats:
Inline:
$f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2$
Equation:
\begin{equation} f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2 \end{equation}
Domain:
$-1 \leq x_i \leq 1$
Reference:
http://infinity77.net/global_optimization/test_functions_nd_C.html#go_benchmark.CosineMixture
"""
Name = ['CosineMixture']
[docs] def __init__(self, lower=-1.0, upper=1.0):
r"""Initialize of Cosine mixture benchmark.
Args:
lower (Optional[float]): Lower bound of problem.
upper (Optional[float]): Upper bound of problem.
See Also:
:func:`niapy.benchmarks.Benchmark.__init__`
"""
super().__init__(lower, upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function.
"""
def f(dimension, x):
r"""Fitness function.
Args:
dimension (int): Dimensionality of the problem
x (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.
Returns:
float: Fitness value for the solution.
"""
v1, v2 = 0.0, 0.0
for i in range(dimension):
v1, v2 = v1 + np.cos(5 * np.pi * x[i]), v2 + x[i] ** 2
return -0.1 * v1 - v2
return f
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