# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Ackley']
[docs]class Ackley(object):
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(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
"""
def __init__(self, Lower=-32.768, Upper=32.768):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
"""Return benchmark evaluation function."""
def evaluate(D, sol):
a = 20 # Recommended variable value
b = 0.2 # Recommended variable value
c = 2 * math.pi # Recommended variable value
val = 0.0
val1 = 0.0
val2 = 0.0
for i in range(D):
val1 += math.pow(sol[i], 2)
val2 += math.cos(c * sol[i])
temp1 = -b * math.sqrt(val1 / D)
temp2 = val2 / D
val = -a * math.exp(temp1) - math.exp(temp2) + a + math.exp(1)
return val
return evaluate