# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['StyblinskiTang']
[docs]class StyblinskiTang(object):
r"""Implementation of Styblinski-Tang functions.
Date: 2018
Authors: Lucija Brezočnik
License: MIT
Function: **Styblinski-Tang function**
:math:`f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left(
x_i^4 - 16x_i^2 + 5x_i \right)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-5, 5]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = -78.332`, at :math:`x^* = (-2.903534,...,-2.903534)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left(
x_i^4 - 16x_i^2 + 5x_i \right) $
Equation:
\begin{equation}f(\mathbf{x}) =
\frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right) \end{equation}
Domain:
$-5 \leq x_i \leq 5$
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=-5.0, Upper=5.0):
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(sol[i], 4) - 16.0 * math.pow(sol[i], 2) + 5.0 * sol[i])
return 0.5 * val
return evaluate