# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
"""Implementations of Alpine functions."""
import math
__all__ = ['Alpine1', 'Alpine2']
[docs]class Alpine1:
r"""Implementation of Alpine1 function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Alpine1 function**
:math:`f(\mathbf{x}) = \sum_{i=1}^{D} |x_i \sin(x_i)+0.1x_i|`
**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:
$f(\mathbf{x}) = \sum_{i=1}^{D} \left |x_i \sin(x_i)+0.1x_i \right|$
Equation:
\begin{equation} f(x) = \sum_{i=1}^{D} \left|x_i \sin(x_i) + 0.1x_i \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.sin(sol[i]) + 0.1 * sol[i])
return val
return evaluate
[docs]class Alpine2:
r"""Implementation of Alpine2 function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Alpine2 function**
:math:`f(\mathbf{x}) = \prod_{i=1}^{D} \sqrt{x_i} \sin(x_i)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [0, 10]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 2.808^D`, at :math:`x^* = (7.917,...,7.917)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \prod_{i=1}^{D} \sqrt{x_i} \sin(x_i)$
Equation:
\begin{equation} f(\mathbf{x}) =
\prod_{i=1}^{D} \sqrt{x_i} \sin(x_i) \end{equation}
Domain:
$0 \leq x_i \leq 10$
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=0.0, Upper=10.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 1.0
for i in range(D):
val *= math.sqrt(sol[i]) * math.sin(sol[i])
return val
return evaluate