# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Whitley']
[docs]class Whitley(object):
r"""Implementation of Whitley function.
Date: 2018
Authors: Grega Vrbančič and Lucija Brezočnik
License: MIT
Function: **Whitley function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \sum_{j=1}^D
\left(\frac{(100(x_i^2-x_j)^2 + (1-x_j)^2)^2}{4000} -
\cos(100(x_i^2-x_j)^2 + (1-x_j)^2)+1\right)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-10.24, 10.24]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (1,...,1)`
LaTeX formats:
Inline:
$f(\mathbf{x}) =
\sum_{i=1}^D \sum_{j=1}^D \left(\frac{(100(x_i^2-x_j)^2 +
(1-x_j)^2)^2}{4000} - \cos(100(x_i^2-x_j)^2 + (1-x_j)^2)+1\right)$
Equation:
\begin{equation}f(\mathbf{x}) =
\sum_{i=1}^D \sum_{j=1}^D \left(\frac{(100(x_i^2-x_j)^2 +
(1-x_j)^2)^2}{4000} - \cos(100(x_i^2-x_j)^2 +
(1-x_j)^2)+1\right) \end{equation}
Domain:
$-10.24 \leq x_i \leq 10.24$
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=-10.24, Upper=10.24):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
for j in range(D):
temp = 100 * \
math.pow((math.pow(sol[i], 2) - sol[j]), 2) + math.pow(
1 - sol[j], 2)
val += (float(math.pow(temp, 2)) / 4000.0) - \
math.cos(temp) + 1
return val
return evaluate