# encoding=utf8
"""Implementation of Griewank funcion."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Griewank', 'ExpandedGriewankPlusRosenbrock']
[docs]class Griewank(Problem):
r"""Implementation of Griewank function.
Date: 2018
Authors: Iztok Fister Jr. and Lucija Brezočnik
License: MIT
Function: **Griewank function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} - \prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} -
\prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1$
Equation:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} -
\prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
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=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Griewank problem..
Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bound of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bound 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'''$f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} - \prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1$'''
def _evaluate(self, x):
val1 = np.sum(x * x / 4000.0)
i = np.arange(1, self.dimension + 1)
val2 = np.product(np.cos(x / np.sqrt(i)))
return val1 - val2 + 1.0
[docs]class ExpandedGriewankPlusRosenbrock(Problem):
r"""Implementation of Expanded Griewank's plus Rosenbrock function.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function: **Expanded Griewank's plus Rosenbrock function**
:math:`f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
LaTeX formats:
Inline:
$f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1$
Equation:
\begin{equation} f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
Reference:
http://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf
"""
[docs] def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Expanded Griewank's plus Rosenbrock 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'''$f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1$'''
def _evaluate(self, x):
x1 = 100.0 * (x[1:] - x[:-1] ** 2.0) ** 2.0 + (1 - x[:-1]) ** 2.0
x2 = x1 * x1 / 4000.0 - np.cos(x1 / np.sqrt(np.arange(1, self.dimension)))
return np.sum(x2)
