Source code for niapy.problems.discus
# encoding=utf8
"""Implementations of Discus functions."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Discus']
[docs]class Discus(Problem):
r"""Implementations of Discus functions.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Discus Function**
:math:`f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^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 ∈ [-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:
$f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^D x_i^2$
Equation:
\begin{equation} f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^D x_i^2 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
Reference:
http://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf
"""
[docs] def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Discus problem..
Args:
dimension (Optional[int]): Dimension of the problem.
lower (Optional[Union[float, Iterable[float]]]): Lower bounds of the problem.
upper (Optional[Union[float, Iterable[float]]]): Upper bounds of the problem.
See Also:
:func:`niapy.problems.Problem.__init__`
"""
super().__init__(dimension, lower, upper, *args, **kwargs)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^D x_i^2$'''
def _evaluate(self, x):
return x[0] * 1000000 + np.sum(np.square(x[1:]))
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