Source code for niapy.problems.schaffer

# encoding=utf8

"""Implementations of Schaffer functions."""

import numpy as np
from niapy.problems.problem import Problem

__all__ = ['SchafferN2', 'SchafferN4', 'ExpandedSchaffer']


[docs]class SchafferN2(Problem): r"""Implementations of Schaffer N. 2 functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Schaffer N. 2 Function** :math:`f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \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^* = (420.968746,...,420.968746)` LaTeX formats: Inline: $f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$ Equation: \begin{equation} f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^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, lower=-100.0, upper=100.0, *args, **kwargs): r"""Initialize SchafferN2 problem.. Args: 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__` """ kwargs.pop('dimension', None) super().__init__(2, lower, upper, *args, **kwargs)
[docs] @staticmethod def latex_code(): r"""Return the latex code of the problem. Returns: str: Latex code. """ return r'''$f(\textbf{x}) = 0.5 + \frac{ \sin^2 \left( x_1^2 - x_2^2 \right) - 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$'''
def _evaluate(self, x): return 0.5 + (np.sin(x[0] ** 2 - x[1] ** 2) ** 2 - 0.5) / (1 + 0.001 * (x[0] ** 2 + x[1] ** 2)) ** 2
[docs]class SchafferN4(Problem): r"""Implementations of Schaffer N. 2 functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Schaffer N. 2 Function** :math:`f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \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^* = (420.968746,...,420.968746)` LaTeX formats: Inline: $f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$ Equation: \begin{equation} f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^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, lower=-100.0, upper=100.0, *args, **kwargs): r"""Initialize SchafferN4 problem.. Args: 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__` """ kwargs.pop('dimension', None) super().__init__(2, lower, upper, *args, **kwargs)
[docs] @staticmethod def latex_code(): r"""Return the latex code of the problem. Returns: str: Latex code. """ return r'''$f(\textbf{x}) = 0.5 + \frac{ \cos^2 \left( \sin \left( x_1^2 - x_2^2 \right) \right)- 0.5 }{ \left( 1 + 0.001 \left( x_1^2 + x_2^2 \right) \right)^2 }$'''
def _evaluate(self, x): return 0.5 + (np.cos(np.sin(x[0] ** 2 - x[1] ** 2)) ** 2 - 0.5) / (1 + 0.001 * (x[0] ** 2 + x[1] ** 2)) ** 2
[docs]class ExpandedSchaffer(Problem): r"""Implementations of Expanded Schaffer functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Expanded Schaffer Function** :math:`f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \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^* = (420.968746,...,420.968746)` LaTeX formats: Inline: $f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2$ Equation: \begin{equation} f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^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 Expanded Schaffer 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'''$f(\textbf{x}) = g(x_D, x_1) + \sum_{i=2}^D g(x_{i - 1}, x_i) \\ g(x, y) = 0.5 + \frac{\sin \left(\sqrt{x^2 + y^2} \right)^2 - 0.5}{\left( 1 + 0.001 (x^2 + y^2) \right)}^2$'''
def _evaluate(self, x): x_next = np.roll(x, -1) tmp = x ** 2 + x_next ** 2 val = 0.5 + (np.sin(np.sqrt(tmp)) ** 2 - 0.5) / (1 + 0.001 * tmp) ** 2 return np.sum(val)