# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['Salomon']
[docs]class Salomon:
r"""Implementation of Salomon function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Salomon function**
:math:`f(\mathbf{x}) = 1 - \cos\left(2\pi\sqrt{\sum_{i=1}^D x_i^2}
\right)+ 0.1 \sqrt{\sum_{i=1}^D 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 ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = f(0, 0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = 1 - \cos\left(2\pi\sqrt{\sum_{i=1}^D x_i^2}
\right)+ 0.1 \sqrt{\sum_{i=1}^D x_i^2}$
Equation:
\begin{equation} f(\mathbf{x}) =
1 - \cos\left(2\pi\sqrt{\sum_{i=1}^D x_i^2}
\right)+ 0.1 \sqrt{\sum_{i=1}^D x_i^2} \end{equation}
Domain:
$-100 \leq x_i \leq 100$
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=-100.0, Upper=100.0):
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)
return 1.0 - math.cos(2.0 * math.pi * math.sqrt(val)) + 0.1 * val
return evaluate