# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Quintic']
[docs]class Quintic:
r"""Implementation of Quintic function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Quintic function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \left| x_i^5 - 3x_i^4 +
4x_i^3 + 2x_i^2 - 10x_i - 4\right|`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = f(-1\; \text{or}\; 2)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left| x_i^5 - 3x_i^4 +
4x_i^3 + 2x_i^2 - 10x_i - 4\right|$
Equation:
\begin{equation} f(\mathbf{x}) =
\sum_{i=1}^D \left| x_i^5 - 3x_i^4 + 4x_i^3 + 2x_i^2 -
10x_i - 4\right| \end{equation}
Domain:
$-10 \leq x_i \leq 10$
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=-10.0, Upper=10.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += abs(math.pow(sol[i], 5) - 3.0 * math.pow(sol[i], 4) + 4.0 *
math.pow(sol[i], 3) + 2.0 * math.pow(sol[i], 2) - 10.0 * sol[i] - 4)
return val
return evaluate