Source code for niapy.problems.pinter
# encoding=utf8
"""Implementation of Pinter function."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Pinter']
[docs]class Pinter(Problem):
r"""Implementation of Pintér function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Pintér function**
:math:`f(\mathbf{x}) =
\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i
\log_{10} (1 + iB^2);`
:math:`A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad`
:math:`B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) =
\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i
\log_{10} (1 + iB^2);
A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad
B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$
Equation:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 +
\sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2);
A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad
B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1) \end{equation}
Domain:
$-10 \leq x_i \leq 10$
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=-10.0, upper=10.0, *args, **kwargs):
r"""Initialize Pinter 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''' $f(\mathbf{x}) =
\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i
\log_{10} (1 + iB^2);
A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad
B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$'''
def _evaluate(self, x):
sub = np.roll(x, 1)
add = np.roll(x, - 1)
indices = np.arange(1, self.dimension + 1)
a = (sub * np.sin(x) + np.sin(add))
b = ((sub * sub) - 2.0 * x + 3.0 * add - np.cos(x) + 1.0)
val1 = np.sum(indices * x * x)
val2 = np.sum(20.0 * indices * np.power(np.sin(a), 2.0))
val3 = np.sum(indices * np.log10(1.0 + indices * np.power(b, 2.0)))
return val1 + val2 + val3