Source code for niapy.problems.sum_squares

# encoding=utf8
"""Sum Squares problem."""

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

__all__ = ['SumSquares']

[docs]class SumSquares(Problem): r"""Implementation of Sum Squares functions. Date: 2018 Authors: Lucija Brezočnik License: MIT Function: **Sum Squares function** :math:`f(\mathbf{x}) = \sum_{i=1}^D i 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 ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`. **Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)` LaTeX formats: Inline: $f(\mathbf{x}) = \sum_{i=1}^D i x_i^2$ Equation: \begin{equation}f(\mathbf{x}) = \sum_{i=1}^D i x_i^2 \end{equation} Domain: $0 \leq x_i \leq 10$ 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=-10.0, upper=10.0, *args, **kwargs): r"""Initialize Sum Squares 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'''$f(\mathbf{x}) = \sum_{i=1}^D i x_i^2$'''
def _evaluate(self, x): return np.sum(np.arange(1, self.dimension + 1) * x ** 2)