# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Qing']
[docs]class Qing(object):
r"""Implementation of Qing function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Qing function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \left(x_i^2 - i\right)^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-500, 500]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (\pm √i))`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left (x_i^2 - i\right)^2$
Equation:
\begin{equation} f(\mathbf{x}) =
\sum_{i=1}^D \left{(x_i^2 - i\right)}^2 \end{equation}
Domain:
$-500 \leq x_i \leq 500$
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=-500.0, Upper=500.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += math.pow(math.pow(sol[i], 2) - i, 2)
return val
return evaluate