Source code for niapy.problems.rastrigin

# encoding=utf8

"""Implementation of Rastrigin function."""

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

__all__ = ['Rastrigin']

[docs]class Rastrigin(Problem): r"""Implementation of Rastrigin problem. Date: 2018 Authors: Lucija Brezočnik and Iztok Fister Jr. License: MIT Function: **Rastrigin function** :math:`f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)` **Input domain:** The function can be defined on any input domain but it is usually evaluated on the hypercube :math:`x_i ∈ [-5.12, 5.12]`, for all :math:`i = 1, 2,..., D`. **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)` LaTeX formats: Inline: $f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$ Equation: \begin{equation} f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right) \end{equation} Domain: $-5.12 \leq x_i \leq 5.12$ Reference: """
[docs] def __init__(self, dimension=4, lower=-5.12, upper=5.12, *args, **kwargs): r"""Initialize Rastrigin 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'''$f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$'''
def _evaluate(self, x): return 10.0 * self.dimension + np.sum(x * x - 10.0 * np.cos(2 * np.pi * x))