Source code for niapy.problems.ridge
# encoding=utf8
"""Implementation of Ridge function."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Ridge']
[docs]class Ridge(Problem):
r"""Implementation of Ridge function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Ridge function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D (\sum_{j=1}^i x_j)^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-64, 64]`, 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 (\sum_{j=1}^i x_j)^2 $
Equation:
\begin{equation} f(\mathbf{x}) =
\sum_{i=1}^D (\sum_{j=1}^i x_j)^2 \end{equation}
Domain:
$-64 \leq x_i \leq 64$
Reference:
http://www.cs.unm.edu/~neal.holts/dga/benchmarkFunction/ridge.html
"""
[docs] def __init__(self, dimension=4, lower=-64.0, upper=64.0, *args, **kwargs):
r"""Initialize Ridge 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 (\sum_{j=1}^i x_j)^2 $'''
def _evaluate(self, x):
inner = np.array([np.sum(x[:i]) for i in range(1, self.dimension + 1)])
return np.sum(inner ** 2)