Source code for NiaPy.benchmarks.happyCat

# encoding=utf8

"""Impementation of Happy Cat funtion."""

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__` """ Benchmark.__init__(self, 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(D, sol): r"""Fitness function. Args: D (int): Dimensionality of the problem sol (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(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