Source code for niapy.problems.zakharov

# encoding=utf8
"""Implementations of Zakharov function."""

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

__all__ = ['Zakharov']


[docs]class Zakharov(Problem): r"""Implementations of Zakharov functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Zakharov Function** :math:`f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4` **Input domain:** The function can be defined on any input domain but it is usually evaluated on the hypercube :math:`x_i ∈ [-5, 10]`, for all :math:`i = 1, 2,..., D`. **Global minimum:** :math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (0, \cdots, 0)` LaTeX formats: Inline: $f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$ Equation: \begin{equation} f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4 \end{equation} Domain: $-5 \leq x_i \leq 10$ Reference: https://www.sfu.ca/~ssurjano/zakharov.html """
[docs] def __init__(self, dimension=4, lower=-5.0, upper=10.0, *args, **kwargs): r"""Initialize Zakharov 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'''$f(\textbf{x}) = \sum_{i = 1}^D x_i^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^2 + \left( \sum_{i = 1}^D 0.5 i x_i \right)^4$'''
def _evaluate(self, x): sum1 = np.sum(x * x) sum2 = np.sum(0.5 * np.arange(1, self.dimension + 1) * x) return sum1 + sum2 ** 2 + sum2 ** 4