# encoding=utf8
"""Implementations of Step functions."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Step', 'Step2', 'Step3']
[docs]class Step(Problem):
r"""Implementation of Step function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Step function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor \left |
x_i \right | \rfloor \right)`
**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^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor \left |
x_i \right | \rfloor \right)$
Equation:
\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor \left | x_i \right | \rfloor \right) \end{equation}
Domain:
$-100 \leq x_i \leq 100$
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.
"""
[docs] def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Step 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'''$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor \left | x_i \right | \rfloor \right)$'''
def _evaluate(self, x):
return np.sum(np.floor(np.abs(x)))
[docs]class Step2(Problem):
r"""Step2 function implementation.
Date: 2018
Author: Lucija Brezočnik
Licence: MIT
Function: **Step2 function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i + 0.5 \rfloor \right)^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^* = (-0.5,...,-0.5)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i + 0.5 \rfloor \right)^2$
Equation:
\begin{equation}f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor x_i + 0.5 \rfloor \right)^2 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
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.
"""
[docs] def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Step2 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'''$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i + 0.5 \rfloor \right)^2$'''
def _evaluate(self, x):
return np.sum(np.floor(x + 0.5) ** 2)
[docs]class Step3(Problem):
r"""Step3 function implementation.
Date: 2018
Author: Lucija Brezočnik
Licence: MIT
Function: **Step3 function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i^2 \rfloor \right)`
**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^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i^2 \rfloor \right)$
Equation:
\begin{equation}f(\mathbf{x}) = \sum_{i=1}^D \left(
\lfloor x_i^2 \rfloor \right)\end{equation}
Domain:
$-100 \leq x_i \leq 100$
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.
"""
[docs] def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs):
r"""Initialize Step3 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'''$f(\mathbf{x}) = \sum_{i=1}^D \left( \lfloor x_i^2 \rfloor \right)$'''
def _evaluate(self, x):
return np.sum(np.floor(x ** 2))