Source code for niapy.problems.qing
# encoding=utf8
"""Implementation of Qing funcion."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Qing']
[docs]class Qing(Problem):
r"""Implementation of Qing function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Qing function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \left(x_i^2 - i\right)^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-500, 500]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (\pm √i))`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left (x_i^2 - i\right)^2$
Equation:
\begin{equation} f(\mathbf{x}) =
\sum_{i=1}^D \left{(x_i^2 - i\right)}^2 \end{equation}
Domain:
$-500 \leq x_i \leq 500$
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=-500.0, upper=500.0, *args, **kwargs):
r"""Initialize Qing 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'''$f(\mathbf{x}) = \sum_{i=1}^D \left (x_i^2 - i\right)^2$'''
def _evaluate(self, x):
return np.sum(np.power(x ** 2.0 - np.arange(1, self.dimension + 1), 2.0))