# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Rastrigin']
[docs]class Rastrigin:
r"""Implementation of Rastrigin benchmark function.
Date: 2018
Authors: Lucija Brezočnik and Iztok Fister Jr.
License: MIT
Function: **Rastrigin function**
:math:`f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-5.12, 5.12]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = 10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)$
Equation:
\begin{equation} f(\mathbf{x}) =
10D + \sum_{i=1}^D \left(x_i^2 -10\cos(2\pi x_i)\right)
\end{equation}
Domain:
$-5.12 \leq x_i \leq 5.12$
Reference: https://www.sfu.ca/~ssurjano/rastr.html
"""
def __init__(self, Lower=-5.12, Upper=5.12):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += math.pow(sol[i], 2) - (10.0 * math.cos(2 * math.pi * sol[i]))
return 10 * D + val
return evaluate