# encoding=utf8
"""Implementations of Michalewichz's function."""
import numpy as np
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['Michalewichz']
[docs]class Michalewichz(Benchmark):
r"""Implementations of Michalewichz's functions.
Date:
2018
Author:
Klemen Berkovič
License:
MIT
Function:
**High Conditioned Elliptic Function**
:math:`f(\textbf{x}) = \sum_{i=1}^D \left( 10^6 \right)^{ \frac{i - 1}{D - 1} } x_i^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [0, \pi]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
at :math:`d = 2` :math:`f(\textbf{x}^*) = -1.8013` at :math:`\textbf{x}^* = (2.20, 1.57)`
at :math:`d = 5` :math:`f(\textbf{x}^*) = -4.687658`
at :math:`d = 10` :math:`f(\textbf{x}^*) = -9.66015`
LaTeX formats:
Inline:
$f(\textbf{x}) = - \sum_{i = 1}^{D} \sin(x_i) \sin\left( \frac{ix_i^2}{\pi} \right)^{2m}$
Equation:
\begin{equation} f(\textbf{x}) = - \sum_{i = 1}^{D} \sin(x_i) \sin\left( \frac{ix_i^2}{\pi} \right)^{2m} \end{equation}
Domain:
$0 \leq x_i \leq \pi$
Attributes:
Name (List[str]): Names of the benchmark.
m (float): Function parameter.
See Also:
* :class:`NiaPy.benchmarks.Benchmark`
Reference URL:
https://www.sfu.ca/~ssurjano/michal.html
"""
Name = ['Michalewichz', 'michalewicz']
m = 10
[docs] def __init__(self, Lower=0.0, Upper=np.pi, m=10, **kwargs):
r"""Initialize of Michalewichz benchmark.
Args:
Lower (Optional[float]): Lower bound of problem.
Upper (Optional[float]): Upper bound of problem.
m (Optional[float]): Function parameter.
kwargs (Dict[str, Any]): Additional arguments.
See Also:
:func:`NiaPy.benchmarks.Benchmark.__init__`
"""
Benchmark.__init__(self, Lower, Upper)
self.m = m
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code
"""
return r'''$f(\textbf{x}) = - \sum_{i = 1}^{D} \sin(x_i) \sin\left( \frac{ix_i^2}{\pi} \right)^{2m}$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, list, numpy.ndarray], Dict[str, Any]], float]: Fitness function
"""
self_m = self.m
def evaluate(D, X, m=None, **kwargs):
r"""Fitness function.
Args:
D (int): Dimensionality of the problem
X (Union[int, float, list, numpy.ndarray]): Solution to check.
m (Optional[float]): Function parameter.
kwargs (Dict[str, Any]): Additional arguments.
Returns:
float: Fitness value for the solution.
"""
m = m if m is not None else self_m
v = 0.0
for i in range(D): v += np.sin(X[i]) * np.sin(((i + 1) * X[i] ** 2) / np.pi) ** (2 * m)
return -v
return evaluate