# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['SumSquares']
[docs]class SumSquares(object):
r"""Implementation of Sum Squares functions.
Date: 2018
Authors: Lucija Brezočnik
License: MIT
Function: **Sum Squares function**
:math:`f(\mathbf{x}) = \sum_{i=1}^D i 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 ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`.
**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = \sum_{i=1}^D i x_i^2$
Equation:
\begin{equation}f(\mathbf{x}) = \sum_{i=1}^D i x_i^2 \end{equation}
Domain:
$0 \leq x_i \leq 10$
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=-10.0, Upper=10.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += i * math.pow(sol[i], 2)
return val
return evaluate