Source code for niapy.problems.cosine_mixture
# encoding=utf8
"""Implementations of Cosine mixture functions."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['CosineMixture']
[docs]class CosineMixture(Problem):
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
"""
[docs] def __init__(self, dimension=4, lower=-1.0, upper=1.0, *args, **kwargs):
r"""Initialize Cosine mixture problem..
Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.
See Also:
:func:`niapy.problems.Problem.__init__`
"""
super().__init__(dimension, lower, upper, *args, **kwargs)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2$'''
def _evaluate(self, x):
return -0.1 * np.sum(np.cos(5 * np.pi * x)) - np.sum(x ** 2)