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# encoding=utf8 |
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"""Implementations of Perm function.""" |
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from NiaPy.benchmarks.benchmark import Benchmark |
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__all__ = ['Perm'] |
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class Perm(Benchmark): |
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r"""Implementations of Perm functions. |
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Date: 2018 |
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Author: Klemen Berkovič |
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License: MIT |
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Arguments: |
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beta {real} -- value added to inner sum of funciton |
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Function: |
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**Perm Function** |
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:math:`f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2` |
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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 ∈ [-D, D]`, for all :math:`i = 1, 2,..., D`. |
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**Global minimum:** |
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:math:`f(\textbf{x}^*) = 0` at :math:`\textbf{x}^* = (1, \frac{1}{2}, \cdots , \frac{1}{i} , \cdots , \frac{1}{D})` |
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LaTeX formats: |
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Inline: |
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$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$ |
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Equation: |
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\begin{equation} f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2 \end{equation} |
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Domain: |
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$-D \leq x_i \leq D$ |
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Reference: |
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https://www.sfu.ca/~ssurjano/perm0db.html |
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""" |
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Name = ['Perm'] |
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def __init__(self, D=10.0, beta=.5): |
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r"""Initialize of Bent Cigar 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, -D, D) |
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Perm.beta = beta |
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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'''$f(\textbf{x}) = \sum_{i = 1}^D \left( \sum_{j = 1}^D (j - \beta) \left( x_j^i - \frac{1}{j^i} \right) \right)^2$''' |
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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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beta = self.beta |
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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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v = .0 |
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for i in range(1, D + 1): |
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vv = .0 |
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for j in range(1, D + 1): vv += (j + beta) * (X[j - 1] ** i - 1 / j ** i) |
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v += vv ** 2 |
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return v |
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return f |
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# vim: tabstop=3 noexpandtab shiftwidth=3 softtabstop=3 |
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NiaOrg /
NiaPy
