# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Griewank']
[docs]class Griewank(object):
r"""Implementation of Griewank function.
Date: 2018
Authors: Iztok Fister Jr. and Lucija Brezočnik
License: MIT
Function: **Griewank function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} - \prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} -
\prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1$
Equation:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} -
\prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
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=-100.0, Upper=100.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val1 = 0.0
val2 = 1.0
for i in range(D):
val1 += (math.pow(sol[i], 2) / 4000.0)
val2 *= (math.cos(sol[i] / math.sqrt(i + 1)))
return val1 - val2 + 1.0
return evaluate