Source code for niapy.problems.elliptic

# encoding=utf8

"""Implementations of High Conditioned Elliptic functions."""

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

__all__ = ['Elliptic']


[docs]class Elliptic(Problem): r"""Implementations of High Conditioned Elliptic functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **High Conditioned Elliptic Function** :math:`f(\textbf{x}) = \sum_{i=1}^D \left( 10^6 \right)^{ \frac{i - 1}{D - 1} } 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^* = (420.968746,...,420.968746)` LaTeX formats: Inline: $f(\textbf{x}) = \sum_{i=1}^D \left( 10^6 \right)^{ \frac{i - 1}{D - 1} } x_i^2$ Equation: \begin{equation} f(\textbf{x}) = \sum_{i=1}^D \left( 10^6 \right)^{ \frac{i - 1}{D - 1} } x_i^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 High Conditioned Elliptic 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'''$f(\textbf{x}) = \sum_{i=1}^D \left( 10^6 \right)^{ \frac{i - 1}{D - 1} } x_i^2$'''
def _evaluate(self, x): indices = np.arange(self.dimension) return np.sum(1000000.0 ** (indices / (self.dimension - 1)) * x)