# encoding=utf8
"""Implementations of Alpine functions."""
import math
from niapy.benchmarks.benchmark import Benchmark
__all__ = ['Alpine1', 'Alpine2']
[docs]class Alpine1(Benchmark):
r"""Implementation of Alpine1 function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Alpine1 function**
:math:`f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert`
**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:
$f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert$
Equation:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert \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.
"""
Name = ['Alpine1']
[docs] def __init__(self, lower=-10.0, upper=10.0):
r"""Initialize of Alpine1 benchmark.
Args:
lower (Optional[float]): Lower bound of problem.
upper (Optional[float]): Upper bound of problem.
See Also:
:func:`niapy.benchmarks.Benchmark.__init__`
"""
super().__init__(lower, upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\mathbf{x}) = \sum_{i=1}^{D} \lvert x_i \sin(x_i)+0.1x_i \rvert$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function
"""
def evaluate(dimension, x):
r"""Fitness function.
Args:
dimension (int): Dimensionality of the problem
x (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.
Returns:
float: Fitness value for the solution.
"""
val = 0.0
for i in range(dimension):
val += abs(math.sin(x[i]) + 0.1 * x[i])
return val
return evaluate
[docs]class Alpine2(Benchmark):
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.
"""
Name = ['Alpine2']
[docs] def __init__(self, lower=0.0, upper=10.0):
r"""Initialize of Alpine2 benchmark.
Args:
lower (Optional[float]): Lower bound of problem.
upper (Optional[float]): Upper bound of problem.
See Also:
:func:`niapy.benchmarks.Benchmark.__init__`
"""
super().__init__(lower=lower, upper=upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\mathbf{x}) = \prod_{i=1}^{D} \sqrt{x_i} \sin(x_i)$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function.
"""
def evaluate(dimension, x):
r"""Fitness function.
Args:
dimension (int): Dimensionality of the problem
x (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.
Returns:
float: Fitness value for the solution.
"""
val = 1.0
for i in range(dimension):
val *= math.sqrt(x[i]) * math.sin(x[i])
return val
return evaluate
