# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Pinter']
[docs]class Pinter(object):
r"""Implementation of Pintér function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Pintér function**
:math:`f(\mathbf{x}) =
\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i
\log_{10} (1 + iB^2);`
:math:`A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad`
:math:`B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)`
**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^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) =
\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i
\log_{10} (1 + iB^2);
A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad
B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$
Equation:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 +
\sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2);
A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad
B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1) \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):
val1 = 0.0
val2 = 0.0
val3 = 0.0
for i in range(D):
if i == 0:
sub = sol[D - 1]
add = sol[i + 1]
elif i == D - 1:
sub = sol[i - 1]
add = sol[0]
else:
sub = sol[i - 1]
add = sol[i + 1]
A = (sub * math.sin(sol[i]) + math.sin(add))
B = (math.pow(sub, 2) - 2.0 * sol[i] + 3.0 * add - math.cos(sol[i]) + 1.0)
val1 += (i + 1.0) * math.pow(sol[i], 2)
val2 += 20.0 * (i + 1.0) * math.pow(math.sin(A), 2)
val3 += (i + 1.0) * math.log10(1.0 + (i + 1.0) * math.pow(B, 2))
return val1 + val2 + val3
return evaluate