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# encoding=utf8 |
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"""Implementations of Cosine mixture functions.""" |
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from numpy import cos, pi |
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from NiaPy.benchmarks.benchmark import Benchmark |
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__all__ = ['CosineMixture'] |
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class CosineMixture(Benchmark): |
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r"""Implementations of Cosine mixture function. |
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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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**Cosine Mixture Function** |
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:math:`f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^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 ∈ [-1, 1]`, for all :math:`i = 1, 2,..., D`. |
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**Global maximu:** |
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:math:`f(x^*) = -0.1 D`, at :math:`x^* = (0.0,...,0.0)` |
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LaTeX formats: |
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Inline: |
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$f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2$ |
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Equation: |
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\begin{equation} f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2 \end{equation} |
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Domain: |
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$-1 \leq x_i \leq 1$ |
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Reference: |
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http://infinity77.net/global_optimization/test_functions_nd_C.html#go_benchmark.CosineMixture |
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""" |
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Name = ['CosineMixture'] |
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def __init__(self, Lower=-1.0, Upper=1.0): |
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r"""Initialize of Cosine mixture 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'''$f(\textbf{x}) = - 0.1 \sum_{i = 1}^D \cos (5 \pi x_i) - \sum_{i = 1}^D x_i^2$''' |
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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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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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v1, v2 = 0.0, 0.0 |
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for i in range(D): v1, v2 = v1 + cos(5 * pi * X[i]), v2 + X[i] ** 2 |
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return -0.1 * v1 - v2 |
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return f |
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# vim: tabstop=3 noexpandtab shiftwidth=3 softtabstop=3 |
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