# encoding=utf8
"""Implementation of Ackley benchmark."""
import numpy as np
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['Ackley']
[docs]class Ackley(Benchmark):
r"""Implementation of Ackley function.
Date: 2018
Author: Lucija Brezočnik and Klemen Berkovič
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
Attributes:
Name (List[str]): Names of the benchmark.
a (float): Objective function argument.
b (float): Objective function argument.
c (float): Objective function argument.
See Also:
* :class:`NiaPy.benchmarks.Benchmark`
"""
Name = ['Ackley', 'ackley']
a = 20 # Recommended variable value
b = 0.2 # Recommended variable value
c = 2 * np.pi # Recommended variable value
[docs] def __init__(self, Lower=-32.768, Upper=32.768, a=20, b=0.2, c=2 * np.pi, **kwargs):
r"""Initialize of Ackley benchmark.
Args:
Lower (Optional[float]): Lower bound of problem.
Upper (Optional[float]): Upper bound of problem.
a (Optional[float]): Objective function argument.
b (Optional[float]): Objective function argument.
c (Optional[float]): Objective function argument.
kwargs (Dict[str, Any]): Additional arguments.
See Also:
:func:`NiaPy.benchmarks.Benchmark.__init__`
"""
Benchmark.__init__(self, Lower, Upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\mathbf{x}) = -a\;\exp\left(-b \sqrt{\frac{1}{D}
\sum_{i=1}^D x_i^2}\right) - \exp\left(\frac{1}{D}
\sum_{i=1}^D cos(c\;x_i)\right) + a + \exp(1)$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, list, numpy.ndarray], Optional[float], Optional[float], Optional[float], Dict[str, Any]], float]: Fitness function
"""
self_a, self_b, self_c = self.a, self.b, self.c
def evaluate(D, sol, a=None, b=None, c=None, **kwargs):
r"""Fitness function.
Args:
D (int): Dimensionality of the problem
sol (Union[int, float, list, numpy.ndarray]): Solution to check.
a (Optional[float]): Function argument.
b (Optional[float]): Function argument.
c (Optional[float]): Function argument.
kwargs (Dict[str, Any]): Additional arguments.
Returns:
float: Fitness value for the solution.
"""
a = a if a is not None else self_a
b = b if b is not None else self_b
c = c if c is not None else self_c
val = 0.0
val1 = 0.0
val2 = 0.0
for i in range(D):
val1 += sol[i] ** 2
val2 += np.cos(c * sol[i])
temp1 = -b * np.sqrt(val1 / D)
temp2 = val2 / D
val = -a * np.exp(temp1) - np.exp(temp2) + a + np.exp(1)
return val
return evaluate