# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Rosenbrock']
[docs]class Rosenbrock:
r"""Implementation of Rosenbrock benchmark function.
Date: 2018
Authors: Iztok Fister Jr. and Lucija Brezočnik
License: MIT
Function: **Rosenbrock function**
:math:`f(\mathbf{x}) = \sum_{i=1}^{D-1} \left (100 (x_{i+1} - x_i^2)^2 + (x_i - 1)^2 \right)`
**Input domain:**
The function can be defined on any input domain but it is usually
evaluated on the hypercube :math:`x_i ∈ [-30, 30]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (1,...,1)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^{D-1} (100 (x_{i+1} - x_i^2)^2 + (x_i - 1)^2)$
Equation:
\begin{equation}
f(\mathbf{x}) = \sum_{i=1}^{D-1} (100 (x_{i+1} - x_i^2)^2 + (x_i - 1)^2)
\end{equation}
Domain:
$-30 \leq x_i \leq 30$
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.
"""
def __init__(self, Lower=-30.0, Upper=30.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D - 1):
val += 100.0 * math.pow(sol[i + 1] - math.pow((sol[i]), 2),
2) + math.pow((sol[i] - 1), 2)
return val
return evaluate