Source code for NiaPy.benchmarks.cosinemixture
# encoding=utf8
"""Implementations of Cosine mixture functions."""
from numpy import cos, pi
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['CosineMixture']
[docs]class CosineMixture(Benchmark):
r"""Implementations of Cosine mixture function.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Cosine Mixture Function**
:math:`f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D 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 ∈ [-1, 1]`, for all :math:`i = 1, 2,..., D`.
**Global maximu:**
:math:`f(x^*) = -0.1 D`, at :math:`x^* = (0.0,...,0.0)`
LaTeX formats:
Inline:
$f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2$
Equation:
\begin{equation} f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2 \end{equation}
Domain:
$-1 \leq x_i \leq 1$
Reference:
http://infinity77.net/global_optimization/test_functions_nd_C.html#go_benchmark.CosineMixture
"""
Name = ['CosineMixture']
[docs] def __init__(self, Lower=-1.0, Upper=1.0):
r"""Initialize of Cosine mixture 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'''$f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function
"""
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.
"""
v1, v2 = 0.0, 0.0
for i in range(D): v1, v2 = v1 + cos(5 * pi * X[i]), v2 + X[i] ** 2
return -0.1 * v1 - v2
return f
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