Source code for niapy.problems.dixon_price

# encoding=utf8

"""Implementations of Dixon Price function."""
import numpy as np

from niapy.problems.problem import Problem

__all__ = ['DixonPrice']


[docs]class DixonPrice(Problem): r"""Implementations of Dixon Price function. Date: 2018 Author: Klemen Berkovič License: MIT Function: **Dixon Price Function** :math:`f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2` **Input domain:** The function can be defined on any input domain but it is usually evaluated on the hypercube :math:`x_i ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`. **Global minimum:** :math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (2^{-\frac{2^1 - 2}{2^1}}, \cdots , 2^{-\frac{2^i - 2}{2^i}} , \cdots , 2^{-\frac{2^D - 2}{2^D}})` LaTeX formats: Inline: $f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2$ Equation: \begin{equation} f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2 \end{equation} Domain: $-10 \leq x_i \leq 10$ Reference: https://www.sfu.ca/~ssurjano/dixonpr.html """
[docs] def __init__(self, dimension=4, lower=-10.0, upper=10.0, *args, **kwargs): r"""Initialize Dixon Price 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'''$f(\textbf{x}) = (x_1 - 1)^2 + \sum_{i = 2}^D i (2x_i^2 - x_{i - 1})^2$'''
def _evaluate(self, x): indices = np.arange(2, self.dimension) val = np.sum(indices * (2 * x[2:] ** 2 - x[1:self.dimension - 1]) ** 2) return (x[0] - 1) ** 2 + val