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)