Source code for niapy.problems.discus

# encoding=utf8

"""Implementations of Discus functions."""
import numpy as np

from niapy.problems.problem import Problem

__all__ = ['Discus']

[docs]class Discus(Problem): r"""Implementations of Discus functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Discus Function** :math:`f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^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^* = (420.968746,...,420.968746)` LaTeX formats: Inline: $f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^D x_i^2$ Equation: \begin{equation} f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^D x_i^2 \end{equation} Domain: $-100 \leq x_i \leq 100$ Reference: """
[docs] def __init__(self, dimension=4, lower=-100.0, upper=100.0, *args, **kwargs): r"""Initialize Discus 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'''$f(\textbf{x}) = x_1^2 10^6 + \sum_{i=2}^D x_i^2$'''
def _evaluate(self, x): return x[0] * 1000000 + np.sum(np.square(x[1:]))