Source code for niapy.problems.salomon

# encoding=utf8

"""Implementation of Salomon function."""

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

__all__ = ['Salomon']

[docs]class Salomon(Problem): r"""Implementation of Salomon function. Date: 2018 Author: Lucija Brezočnik License: MIT Function: **Salomon function** :math:`f(\mathbf{x}) = 1 - \cos\left(2\pi\sqrt{\sum_{i=1}^D x_i^2} \right)+ 0.1 \sqrt{\sum_{i=1}^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^* = f(0, 0)` LaTeX formats: Inline: $f(\mathbf{x}) = 1 - \cos\left(2\pi\sqrt{\sum_{i=1}^D x_i^2} \right)+ 0.1 \sqrt{\sum_{i=1}^D x_i^2}$ Equation: \begin{equation} f(\mathbf{x}) = 1 - \cos\left(2\pi\sqrt{\sum_{i=1}^D x_i^2} \right)+ 0.1 \sqrt{\sum_{i=1}^D x_i^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 Salomon 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'''$f(\mathbf{x}) = 1 - \cos\left(2\pi\sqrt{\sum_{i=1}^D x_i^2} \right)+ 0.1 \sqrt{\sum_{i=1}^D x_i^2}$'''
def _evaluate(self, x): val = np.sum(x ** 2.0) return 1.0 - np.cos(2.0 * np.pi * np.sqrt(val)) + 0.1 * val