Source code for niapy.problems.step

# 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))