86 lines
2.6 KiB
Python
86 lines
2.6 KiB
Python
# -*- coding: utf-8 -*-
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from numpy import sum, cos, sin, log
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from .go_benchmark import Benchmark
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class VenterSobiezcczanskiSobieski(Benchmark):
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r"""
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Venter Sobiezcczanski-Sobieski objective function.
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This class defines the Venter Sobiezcczanski-Sobieski [1]_ global optimization
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problem. This is a multimodal minimization problem defined as follows:
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.. math::
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f_{\text{VenterSobiezcczanskiSobieski}}(x) = x_1^2 - 100 \cos^2(x_1)
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- 100 \cos(x_1^2/30)
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+ x_2^2 - 100 \cos^2(x_2)
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- 100 \cos(x_2^2/30)
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with :math:`x_i \in [-50, 50]` for :math:`i = 1, 2`.
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*Global optimum*: :math:`f(x) = -400` for :math:`x = [0, 0]`
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.. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions
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For Global Optimization Problems Int. Journal of Mathematical Modelling
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and Numerical Optimisation, 2013, 4, 150-194.
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TODO Jamil #160 hasn't written the equation very well. Normally a cos
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squared term is written as cos^2(x) rather than cos(x)^2
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"""
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def __init__(self, dimensions=2):
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Benchmark.__init__(self, dimensions)
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self._bounds = list(zip([-50.0] * self.N, [50.0] * self.N))
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self.custom_bounds = ([-10, 10], [-10, 10])
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self.global_optimum = [[0.0 for _ in range(self.N)]]
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self.fglob = -400
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def fun(self, x, *args):
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self.nfev += 1
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u = x[0] ** 2.0 - 100.0 * cos(x[0]) ** 2.0
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v = -100.0 * cos(x[0] ** 2.0 / 30.0) + x[1] ** 2.0
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w = - 100.0 * cos(x[1]) ** 2.0 - 100.0 * cos(x[1] ** 2.0 / 30.0)
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return u + v + w
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class Vincent(Benchmark):
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r"""
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Vincent objective function.
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This class defines the Vincent [1]_ global optimization problem. This
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is a multimodal minimization problem defined as follows:
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.. math::
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f_{\text{Vincent}}(x) = - \sum_{i=1}^{n} \sin(10 \log(x))
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Here, :math:`n` represents the number of dimensions and
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:math:`x_i \in [0.25, 10]` for :math:`i = 1, ..., n`.
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*Global optimum*: :math:`f(x) = -n` for :math:`x_i = 7.70628098`
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for :math:`i = 1, ..., n`
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.. [1] Gavana, A. Global Optimization Benchmarks and AMPGO retrieved 2015
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"""
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def __init__(self, dimensions=2):
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Benchmark.__init__(self, dimensions)
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self._bounds = list(zip([0.25] * self.N, [10.0] * self.N))
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self.global_optimum = [[7.70628098 for _ in range(self.N)]]
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self.fglob = -float(self.N)
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self.change_dimensionality = True
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def fun(self, x, *args):
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self.nfev += 1
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return -sum(sin(10.0 * log(x)))
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