# encoding=utf8
"""Stybliski Tang benchmark."""
import math
from NiaPy.benchmarks.benchmark import Benchmark
__all__ = ['StyblinskiTang']
[docs]class StyblinskiTang(Benchmark):
r"""Implementation of Styblinski-Tang functions.
Date: 2018
Authors: Lucija Brezočnik
License: MIT
Function: **Styblinski-Tang function**
:math:`f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left(
x_i^4 - 16x_i^2 + 5x_i \right)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-5, 5]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = -78.332`, at :math:`x^* = (-2.903534,...,-2.903534)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left(
x_i^4 - 16x_i^2 + 5x_i \right) $
Equation:
\begin{equation}f(\mathbf{x}) =
\frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right) \end{equation}
Domain:
$-5 \leq x_i \leq 5$
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 = ['StyblinskiTang']
[docs] def __init__(self, Lower=-5.0, Upper=5.0):
r"""Initialize of Styblinski Tang 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}) = \frac{1}{2} \sum_{i=1}^D \left(
x_i^4 - 16x_i^2 + 5x_i \right) $'''
[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.
"""
val = 0.0
for i in range(D):
val += (math.pow(sol[i], 4) - 16.0 * math.pow(sol[i], 2) + 5.0 * sol[i])
return 0.5 * val
return evaluate