Source code for niapy.problems.zakharov
# encoding=utf8
"""Implementations of Zakharov function."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Zakharov']
[docs]class Zakharov(Problem):
r"""Implementations of Zakharov functions.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Zakharov Function**
:math:`f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-5, 10]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (0, \cdots, 0)`
LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$
Equation:
\begin{equation} f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4 \end{equation}
Domain:
$-5 \leq x_i \leq 10$
Reference:
https://www.sfu.ca/~ssurjano/zakharov.html
"""
[docs] def __init__(self, dimension=4, lower=-5.0, upper=10.0, *args, **kwargs):
r"""Initialize Zakharov 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'''$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$'''
def _evaluate(self, x):
sum1 = np.sum(x * x)
sum2 = np.sum(0.5 * np.arange(1, self.dimension + 1) * x)
return sum1 + sum2 ** 2 + sum2 ** 4