# encoding=utf8
# pylint: disable=anomalous-backslash-in-string
import math
__all__ = ['HappyCat']
[docs]class HappyCat(object):
r"""Implementation of Happy cat function.
Date: 2018
Author: Lucija Brezočnik
License: MIT
Function: **Happy cat function**
:math:`f(\mathbf{x}) = {\left |\sum_{i = 1}^D {x_i}^2 - D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 + \sum_{i = 1}^D x_i) / D + 0.5`
**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^* = (-1,...,-1)`
LaTeX formats:
Inline:
$f(\mathbf{x}) = {\left|\sum_{i = 1}^D {x_i}^2 -
D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 +
\sum_{i = 1}^D x_i) / D + 0.5$
Equation:
\begin{equation} f(\mathbf{x}) = {\left| \sum_{i = 1}^D {x_i}^2 -
D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 +
\sum_{i = 1}^D x_i) / D + 0.5 \end{equation}
Domain:
$-100 \leq x_i \leq 100$
Reference: http://bee22.com/manual/tf_images/Liang%20CEC2014.pdf
"""
def __init__(self, Lower=-100.0, Upper=100.0):
self.Lower = Lower
self.Upper = Upper
[docs] @classmethod
def function(cls):
def evaluate(D, sol):
val1 = 0.0
val2 = 0.0
alpha = 0.125
for i in range(D):
val1 += math.pow(abs(math.pow(sol[i], 2) - D), alpha)
val2 += (0.5 * math.pow(sol[i], 2) + sol[i]) / D
return val1 + val2 + 0.5
return evaluate