Source code for niapy.problems.perm
# encoding=utf8
"""Implementations of Perm function."""
import numpy as np
from niapy.problems.problem import Problem
__all__ = ['Perm']
[docs]class Perm(Problem):
r"""Implementations of Perm functions.
Date: 2018
Author: Klemen Berkovič
License: MIT
Function:
**Perm Function**
:math:`f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-D, D]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:**
:math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (1, \frac{1}{2}, \cdots , \frac{1}{i} , \cdots , \frac{1}{D})`
LaTeX formats:
Inline:
$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$
Equation:
\begin{equation} f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2 \end{equation}
Domain:
$-D \leq x_i \leq D$
Reference:
https://www.sfu.ca/~ssurjano/perm0db.html
"""
[docs] def __init__(self, dimension=4, beta=0.5, *args, **kwargs):
r"""Initialize Perm problem.
Args:
dimension (Optional[int]): Dimension of the problem.
beta (Optional[float]): Beta parameter.
See Also:
:func:`niapy.problems.Problem.__init__`
"""
super().__init__(dimension, -dimension, dimension, *args, **kwargs)
self.beta = beta
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$'''
def _evaluate(self, x):
ii = np.arange(1, self.dimension + 1)
jj = np.tile(ii, (self.dimension, 1))
x_matrix = np.tile(x, (self.dimension, 1))
inner = np.sum((jj + self.beta) * (np.power(x_matrix, ii) - np.power(1.0 / jj, ii)), axis=0)
return np.sum(inner ** 2)