Source code for niapy.problems.styblinski_tang

# encoding=utf8

"""Styblinski Tang problem."""

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

__all__ = ['StyblinskiTang']

[docs]class StyblinskiTang(Problem): r"""Implementation of Styblinski-Tang functions. Date: 2018 Authors: Lucija Brezočnik License: MIT Function: **Styblinski-Tang function** :math:`f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_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, 5]`, for all :math:`i = 1, 2,..., D`. **Global minimum:** :math:`f(x^*) = -78.332`, at :math:`x^* = (-2.903534,...,-2.903534)` LaTeX formats: Inline: $f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right) $ Equation: \begin{equation}f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right) \end{equation} Domain: $-5 \leq x_i \leq 5$ 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=-5.0, upper=5.0, *args, **kwargs): r"""Initialize Styblinski Tang 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}) = \frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right) $'''
def _evaluate(self, x): return 0.5 * np.sum(x ** 4 - 16.0 * x ** 2 + 5.0 * x)