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# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
"""Implementation of Sphere functions.
Date: 2018
Authors: Iztok Fister Jr.
License: MIT
Function: Sphere function
Input domain:
The function can be defined on any input domain but it is usually
evaluated on the hypercube x_i ∈ [0, 10], for all i = 1, 2,..., D.
Global minimum:
f(x*) = 0, at x* = (0,...,0)
LaTeX formats:
Inline: $f(x) = \sum_{i=1}^D x_i^2$
Equation: \begin{equation}f(x) = \sum_{i=1}^D 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.
"""
import math
__all__ = ['Sphere']
class Sphere(object):
def __init__(self, Lower=-5.12, Upper=5.12):
self.Lower = Lower
self.Upper = Upper
@classmethod
def function(cls):
def evaluate(D, sol):
val = 0.0
for i in range(D):
val += math.pow(sol[i], 2)
return val
return evaluate
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