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# encoding=utf8 |
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"""Implementation of Pinter function.""" |
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import math |
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from NiaPy.benchmarks.benchmark import Benchmark |
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__all__ = ['Pinter'] |
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class Pinter(Benchmark): |
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r"""Implementation of Pintér function. |
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Date: 2018 |
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Author: Lucija Brezočnik |
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License: MIT |
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Function: **Pintér function** |
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:math:`f(\mathbf{x}) = |
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\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i |
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\log_{10} (1 + iB^2);` |
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:math:`A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad` |
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:math:`B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)` |
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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 ∈ [-10, 10]`, for all :math:`i = 1, 2,..., D`. |
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**Global minimum:** :math:`f(x^*) = 0`, at :math:`x^* = (0,...,0)` |
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LaTeX formats: |
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Inline: |
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$f(\mathbf{x}) = |
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\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i |
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\log_{10} (1 + iB^2); |
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A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad |
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B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$ |
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Equation: |
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\begin{equation} f(\mathbf{x}) = \sum_{i=1}^D ix_i^2 + |
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\sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i \log_{10} (1 + iB^2); |
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A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad |
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B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1) \end{equation} |
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Domain: |
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$-10 \leq x_i \leq 10$ |
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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 = ['Pinter'] |
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def __init__(self, Lower=-10.0, Upper=10.0): |
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r"""Initialize of Pinter 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''' $f(\mathbf{x}) = |
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\sum_{i=1}^D ix_i^2 + \sum_{i=1}^D 20i \sin^2 A + \sum_{i=1}^D i |
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\log_{10} (1 + iB^2); |
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A = (x_{i-1}\sin(x_i)+\sin(x_{i+1}))\quad \text{and} \quad |
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B = (x_{i-1}^2 - 2x_i + 3x_{i+1} - \cos(x_i) + 1)$''' |
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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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val1 = 0.0 |
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val2 = 0.0 |
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val3 = 0.0 |
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for i in range(D): |
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if i == 0: |
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sub = sol[D - 1] |
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add = sol[i + 1] |
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elif i == D - 1: |
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sub = sol[i - 1] |
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add = sol[0] |
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else: |
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sub = sol[i - 1] |
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add = sol[i + 1] |
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A = (sub * math.sin(sol[i]) + math.sin(add)) |
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B = (math.pow(sub, 2) - 2.0 * sol[i] + 3.0 * add - math.cos(sol[i]) + 1.0) |
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val1 += (i + 1.0) * math.pow(sol[i], 2) |
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val2 += 20.0 * (i + 1.0) * math.pow(math.sin(A), 2) |
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val3 += (i + 1.0) * math.log10(1.0 + (i + 1.0) * math.pow(B, 2)) |
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return val1 + val2 + val3 |
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return evaluate |
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NiaOrg /
NiaPy
