Source code for niapy.problems.csendes

# encoding=utf8

"""Implementation of Csendes function."""

import numpy as np
from niapy.problems.problem import Problem

__all__ = ['Csendes']

[docs]class Csendes(Problem): r"""Implementation of Csendes function. Date: 2018 Author: Lucija Brezočnik License: MIT Function: **Csendes function** :math:`f(\mathbf{x}) = \sum_{i=1}^D x_i^6\left( 2 + \sin \frac{1}{x_i}\right)` **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 minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)` LaTeX formats: Inline: $f(\mathbf{x}) = \sum_{i=1}^D x_i^6\left( 2 + \sin \frac{1}{x_i}\right)$ Equation: \begin{equation} f(\mathbf{x}) = \sum_{i=1}^D x_i^6\left( 2 + \sin \frac{1}{x_i}\right) \end{equation} Domain: $-1 \leq x_i \leq 1$ Reference paper: Jamil, M., and Yang, X. S. (2013). A literature survey of benchmark functions for global optimisation problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4(2), 150-194. """
[docs] def __init__(self, dimension=4, lower=-1.0, upper=1.0, *args, **kwargs): r"""Initialize Csendes 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'''$f(\mathbf{x}) = \sum_{i=1}^D x_i^6\left( 2 + \sin \frac{1}{x_i}\right)$'''
def _evaluate(self, x): mask = x != 0 return np.sum(np.power(x[mask], 6.0) * (2.0 + np.sin(1.0 / x[mask])))