Source code for niapy.benchmarks.happy_cat
# encoding=utf8
"""Implementation of Happy Cat function."""
import math
from niapy.benchmarks.benchmark import Benchmark
__all__ = ['HappyCat']
[docs]class HappyCat(Benchmark):
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 &
Beyer, H. G., & Finck, S. (2012). HappyCat - A Simple Function Class Where Well-Known Direct Search Algorithms Do Fail.
In International Conference on Parallel Problem Solving from Nature (pp. 367-376). Springer, Berlin, Heidelberg.
"""
Name = ['HappyCat']
[docs] def __init__(self, lower=-100.0, upper=100.0):
r"""Initialize of Happy cat benchmark.
Args:
lower (Optional[float]): Lower bound of problem.
upper (Optional[float]): Upper bound of problem.
See Also:
:func:`niapy.benchmarks.Benchmark.__init__`
"""
super().__init__(lower, upper)
[docs] @staticmethod
def latex_code():
r"""Return the latex code of the problem.
Returns:
str: Latex code.
"""
return r'''$f(\mathbf{x}) = {\left|\sum_{i = 1}^D {x_i}^2 -
D \right|}^{1/4} + (0.5 \sum_{i = 1}^D {x_i}^2 +
\sum_{i = 1}^D x_i) / D + 0.5$'''
[docs] def function(self):
r"""Return benchmark evaluation function.
Returns:
Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function.
"""
def evaluate(dimension, x):
r"""Fitness function.
Args:
dimension (int): Dimensionality of the problem
x (Union[int, float, List[int, float], numpy.ndarray]): Solution to check.
Returns:
float: Fitness value for the solution.
"""
val1 = 0.0
val2 = 0.0
alpha = 0.125
for i in range(dimension):
val1 += math.pow(abs(math.pow(x[i], 2) - dimension), alpha)
val2 += (0.5 * math.pow(x[i], 2) + x[i]) / dimension
return val1 + val2 + 0.5
return evaluate