Source code for NiaPy.benchmarks.zakharov
# encoding=utf8
"""Implementations of Zakharov function."""
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['Zakharov']
[docs]class Zakharov(Benchmark):
r"""Implementations of Zakharov functions.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Levy Function**
:math:`f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-5, 10]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (0, \cdots, 0)`
LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$
Equation:
\begin{equation} f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4 \end{equation}
Domain:
$-5 \leq x_i \leq 10$
Reference:
https://www.sfu.ca/~ssurjano/levy.html
"""
Name = ['Zakharov']
[docs] def __init__(self, Lower=-5.0, Upper=10.0):
r"""Initialize of Zakharov 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'''$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$'''
[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
X (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 + X[i] ** 2, v2 + 0.5 * (i + 1) * X[i]
return v1 + v2 ** 2 + v2 ** 4
return f
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