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"""Implementation of Griewank funcion."""
from math import sqrt, cos
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['Griewank', 'ExpandedGriewankPlusRosenbrock']
[docs]class Griewank(Benchmark):
r"""Implementation of Griewank function.
Date: 2018
Authors: Iztok Fister Jr. and Lucija Brezočnik
License: MIT
Function: **Griewank function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} - \prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} -
\prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1$
Equation:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} -
\prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
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 = ['Griewank']
[docs] def __init__(self, Lower=-100.0, Upper=100.0):
r"""Initialize of Griewank benchmark.
Args:
Lower (Optional[float]): Lower bound of problem.
Upper (Optional[float]): Upper bound of problem.
See Also:
:func:`NiaPy.benchmarks.Benchmark.__init__`
"""
Benchmark.__init__(self, Lower, Upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\mathbf{x}) = \sum_{i=1}^D \frac{x_i^2}{4000} -
\prod_{i=1}^D \cos(\frac{x_i}{\sqrt{i}}) + 1$'''
[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(D, sol):
r"""Fitness function.
Args:
D (int): Dimensionality of the problem
sol (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.
Returns:
float: Fitness value for the solution.
"""
val1, val2 = 0.0, 1.0
for i in range(D):
val1 += sol[i] ** 2 / 4000.0
val2 *= cos(sol[i] / sqrt(i + 1))
return val1 - val2 + 1.0
return evaluate
[docs]class ExpandedGriewankPlusRosenbrock(Benchmark):
r"""Implementation of Expanded Griewank's plus Rosenbrock function.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function: **Expanded Griewank's plus Rosenbrock function**
:math:`f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)`
LaTeX formats:
Inline:
$f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1$
Equation:
\begin{equation} f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
Reference:
http://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf
"""
Name = ['ExpandedGriewankPlusRosenbrock']
[docs] def __init__(self, Lower=-100.0, Upper=100.0):
r"""Initialize of Expanded Griewank's plus Rosenbrock benchmark.
Args:
Lower (Optional[float]): Lower bound of problem.
Upper (Optional[float]): Upper bound of problem.
See Also:
:func:`NiaPy.benchmarks.Benchmark.__init__`
"""
Benchmark.__init__(self, Lower, Upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\textbf{x}) = h(g(x_D, x_1)) + \sum_{i=2}^D h(g(x_{i - 1}, x_i)) \\ g(x, y) = 100 (x^2 - y)^2 + (x - 1)^2 \\ h(z) = \frac{z^2}{4000} - \cos \left( \frac{z}{\sqrt{1}} \right) + 1$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function
"""
def h(z): return z ** 2 / 4000 - cos(z / sqrt(1)) + 1
def g(x, y): return 100 * (x ** 2 - y ** 2) ** 2 + (x - 1) ** 2
def f(D, x):
r"""Fitness function.
Args:
D (int): Dimensionality of the problem
sol (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(1, D): val += h(g(x[i - 1], x[i]))
return h(g(x[D - 1], x[0])) + val
return f
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