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# encoding=utf8 |
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"""Stybliski Tang benchmark.""" |
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import math |
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from NiaPy.benchmarks.benchmark import Benchmark |
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__all__ = ['StyblinskiTang'] |
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View Code Duplication |
class StyblinskiTang(Benchmark): |
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r"""Implementation of Styblinski-Tang functions. |
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Date: 2018 |
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Authors: Lucija Brezočnik |
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License: MIT |
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Function: **Styblinski-Tang function** |
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:math:`f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( |
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x_i^4 - 16x_i^2 + 5x_i \right)` |
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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 ∈ [-5, 5]`, for all :math:`i = 1, 2,..., D`. |
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**Global minimum:** :math:`f(x^*) = -78.332`, at :math:`x^* = (-2.903534,...,-2.903534)` |
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LaTeX formats: |
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Inline: |
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$f(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( |
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x_i^4 - 16x_i^2 + 5x_i \right) $ |
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Equation: |
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\begin{equation}f(\mathbf{x}) = |
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\frac{1}{2} \sum_{i=1}^D \left( x_i^4 - 16x_i^2 + 5x_i \right) \end{equation} |
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Domain: |
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$-5 \leq x_i \leq 5$ |
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Reference paper: |
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Jamil, M., and Yang, X. S. (2013). |
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A literature survey of benchmark functions for global optimisation problems. |
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International Journal of Mathematical Modelling and Numerical Optimisation, |
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4(2), 150-194. |
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""" |
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Name = ['StyblinskiTang'] |
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def __init__(self, Lower=-5.0, Upper=5.0): |
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r"""Initialize of Styblinski Tang 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(\mathbf{x}) = \frac{1}{2} \sum_{i=1}^D \left( |
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x_i^4 - 16x_i^2 + 5x_i \right) $''' |
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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 evaluate(D, sol): |
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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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val = 0.0 |
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for i in range(D): |
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val += (math.pow(sol[i], 4) - 16.0 * math.pow(sol[i], 2) + 5.0 * sol[i]) |
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return 0.5 * val |
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return evaluate |
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