# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Csendes']
[docs]class Csendes:
r"""Implementation of Csendes function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Csendes function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D x_i^6\left( 2 + \sin \frac{1}{x_i}\right)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-1, 1]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D x_i^6\left( 2 + \sin \frac{1}{x_i}\right)$
Equation:
\begin{equation} f(\mathbf{x}) =
\sum_{i=1}^D x_i^6\left( 2 + \sin \frac{1}{x_i}\right) \end{equation}
Domain:
$-1 \leq x_i \leq 1$
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.
"""
def __init__(self, Lower=-1.0, Upper=1.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
if sol[i] != 0:
val += math.pow(sol[i], 6) * (2.0 + math.sin(1.0 / sol[i]))
return val
return evaluate