Source code for niapy.problems.ackley
# encoding=utf8
"""Implementation of Ackley problem."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Ackley']
[docs]class Ackley(Problem):
r"""Implementation of Ackley function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Ackley function**
:math:`f(\mathbf{x}) = -a\;\exp\left(-b \sqrt{\frac{1}{D}\sum_{i=1}^D x_i^2}\right)
- \exp\left(\frac{1}{D}\sum_{i=1}^D \cos(c\;x_i)\right) + a + \exp(1)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-32.768, 32.768]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(\textbf{x}^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = -a\;\exp\left(-b \sqrt{\frac{1}{D}
\sum_{i=1}^D x_i^2}\right) - \exp\left(\frac{1}{D}
\sum_{i=1}^D cos(c\;x_i)\right) + a + \exp(1)$
Equation:
\begin{equation}f(\mathbf{x}) =
-a\;\exp\left(-b \sqrt{\frac{1}{D} \sum_{i=1}^D x_i^2}\right) -
\exp\left(\frac{1}{D} \sum_{i=1}^D \cos(c\;x_i)\right) +
a + \exp(1) \end{equation}
Domain:
$-32.768 \leq x_i \leq 32.768$
Reference:
https://www.sfu.ca/~ssurjano/ackley.html
"""
[docs] def __init__(self, dimension=4, lower=-32.768, upper=32.768, a=20.0, b=0.2, c=2 * np.pi, *args, **kwargs):
r"""Initialize Ackley 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.
a (Optional[float]): a parameter.
b (Optional[float]): b parameter.
c (Optional[float]): c parameter.
See Also:
:func:`niapy.problems.Problem.__init__`
"""
super().__init__(dimension, lower, upper, *args, **kwargs)
self.a = a
self.b = b
self.c = c
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\mathbf{x}) = -a\;\exp\left(-b \sqrt{\frac{1}{D}
\sum_{i=1}^D x_i^2}\right) - \exp\left(\frac{1}{D}
\sum_{i=1}^D \cos(c\;x_i)\right) + a + \exp(1)$'''
def _evaluate(self, x):
val1 = np.sum(np.square(x))
val2 = np.sum(np.cos(self.c * x))
temp1 = -self.b * np.sqrt(val1 / self.dimension)
temp2 = val2 / self.dimension
return -self.a * np.exp(temp1) - np.exp(temp2) + self.a + np.exp(1)