Source code for niapy.problems.rastrigin
# encoding=utf8
"""Implementation of Rastrigin function."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Rastrigin']
[docs]class Rastrigin(Problem):
r"""Implementation of Rastrigin problem.
Date: 2018
Authors: Lucija Brezočnik and Iztok Fister Jr.
License: MIT
Function: **Rastrigin function**
:math:`f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi 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 ∈ [-5.12, 5.12]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$
Equation:
\begin{equation} f(\mathbf{x}) =
10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)
\end{equation}
Domain:
$-5.12 \leq x_i \leq 5.12$
Reference:
https://www.sfu.ca/~ssurjano/rastr.html
"""
[docs] def __init__(self, dimension=4, lower=-5.12, upper=5.12, *args, **kwargs):
r"""Initialize Rastrigin 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'''$f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$'''
def _evaluate(self, x):
return 10.0 * self.dimension + np.sum(x * x - 10.0 * np.cos(2 * np.pi * x))