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# encoding=utf8 |
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"""Implementations of HGBat functions.""" |
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from math import fabs |
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from NiaPy.benchmarks.benchmark import Benchmark |
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__all__ = ['HGBat'] |
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class HGBat(Benchmark): |
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r"""Implementations of HGBat functions. |
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Date: 2018 |
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Author: Klemen Berkovič |
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License: MIT |
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Function: |
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**HGBat Function** |
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: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` |
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**Input domain:** |
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The function can be defined on any input domain but it is usually |
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evaluated on the hypercube :math:`x_i ∈ [-100, 100]`, for all :math:`i = 1, 2,..., D`. |
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**Global minimum:** |
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:math:`f(x^*) = 0`, at :math:`x^* = (420.968746,...,420.968746)` |
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LaTeX formats: |
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Inline: |
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$$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 |
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Equation: |
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\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} |
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Domain: |
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$-100 \leq x_i \leq 100$ |
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Reference: |
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http://www5.zzu.edu.cn/__local/A/69/BC/D3B5DFE94CD2574B38AD7CD1D12_C802DAFE_BC0C0.pdf |
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""" |
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Name = ['HGBat'] |
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def __init__(self, Lower=-100.0, Upper=100.0): |
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r"""Initialize of HGBat benchmark. |
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Args: |
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Lower (Optional[float]): Lower bound of problem. |
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Upper (Optional[float]): Upper bound of problem. |
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See Also: |
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:func:`NiaPy.benchmarks.Benchmark.__init__` |
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""" |
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Benchmark.__init__(self, Lower, Upper) |
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@staticmethod |
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def latex_code(): |
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r"""Return the latex code of the problem. |
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Returns: |
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str: Latex code |
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""" |
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return r'''$f(\textbf{x}) = \left| \left( \sum_{i=1}^D x_i^2 \right)^2 - \left( \sum_{i=1}^D x_i \right)^2 \right|^{\frac{1}{2}} + \frac{0.5 \sum_{i=1}^D x_i^2 + \sum_{i=1}^D x_i}{D} + 0.5$''' |
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def function(self): |
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r"""Return benchmark evaluation function. |
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Returns: |
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Callable[[int, Union[int, float, List[int, float], numpy.ndarray]], float]: Fitness function |
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""" |
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def f(D, x): |
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r"""Fitness function. |
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Args: |
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D (int): Dimensionality of the problem |
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sol (Union[int, float, List[int, float], numpy.ndarray]): Solution to check. |
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Returns: |
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float: Fitness value for the solution. |
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""" |
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val1, val2 = 0.0, 0.0 |
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for i in range(D): val1 += x[i] ** 2 |
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for i in range(D): val2 += x[i] |
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return fabs(val1 ** 2 - val2 ** 2) ** (1 / 2) + (0.5 * val1 + val2) / D + 0.5 |
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return f |
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# vim: tabstop=3 noexpandtab shiftwidth=3 softtabstop=3 |
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NiaOrg /
NiaPy
