Source code for NiaPy.benchmarks.hgbat

# encoding=utf8

"""Implementations of HGBat functions."""

from math import fabs
from NiaPy.benchmarks.benchmark import Benchmark

__all__ = ['HGBat']

[docs]class HGBat(Benchmark): r"""Implementations of HGBat functions. Date: 2018 Author: Klemen Berkovič License: MIT Function: **HGBat Function** :math:`f(\textbf{x}) = \left| \left( \sum_{i=1}^D x_i^2 \right)^2 - \left( \sum_{i=1}^D x_i \right)^2 \right|^{\frac{1}{2}} + \frac{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^* = (420.968746,...,420.968746)` LaTeX formats: Inline: $$f(\textbf{x}) = \left| \left( \sum_{i=1}^D x_i^2 \right)^2 - \left( \sum_{i=1}^D x_i \right)^2 \right|^{\frac{1}{2}} + \frac{0.5 \sum_{i=1}^D x_i^2 + \sum_{i=1}^D x_i}{D} + 0.5 Equation: \begin{equation} f(\textbf{x}) = \left| \left( \sum_{i=1}^D x_i^2 \right)^2 - \left( \sum_{i=1}^D x_i \right)^2 \right|^{\frac{1}{2}} + \frac{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://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf """ Name = ['HGBat']
[docs] def __init__(self, Lower=-100.0, Upper=100.0): r"""Initialize of HGBat 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'''$f(\textbf{x}) = \left| \left( \sum_{i=1}^D x_i^2 \right)^2 - \left( \sum_{i=1}^D x_i \right)^2 \right|^{\frac{1}{2}} + \frac{0.5 \sum_{i=1}^D x_i^2 + \sum_{i=1}^D x_i}{D} + 0.5$'''
[docs] def function(self): r"""Return benchmark evaluation function. Returns: Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function """ def f(D, x): 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, val2 = 0.0, 0.0 for i in range(D): val1 += x[i] ** 2 for i in range(D): val2 += x[i] return fabs(val1 ** 2 - val2 ** 2) ** (1 / 2) + (0.5 * val1 + val2) / D + 0.5 return f
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