126 lines
3.8 KiB
Python
126 lines
3.8 KiB
Python
# -*- coding: utf-8 -*-
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from numpy import abs, sum, arange, sqrt
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from .go_benchmark import Benchmark
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class Qing(Benchmark):
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r"""
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Qing objective function.
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This class defines the Qing [1]_ global optimization problem. This is a
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multimodal minimization problem defined as follows:
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.. math::
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f_{\text{Qing}}(x) = \sum_{i=1}^{n} (x_i^2 - i)^2
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Here, :math:`n` represents the number of dimensions and
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:math:`x_i \in [-500, 500]` for :math:`i = 1, ..., n`.
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*Global optimum*: :math:`f(x) = 0` for :math:`x_i = \pm \sqrt(i)` for
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:math:`i = 1, ..., n`
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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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"""
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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([-500.0] * self.N,
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[500.0] * self.N))
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self.custom_bounds = [(-2, 2), (-2, 2)]
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self.global_optimum = [[sqrt(_) for _ in range(1, self.N + 1)]]
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self.fglob = 0
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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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i = arange(1, self.N + 1)
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return sum((x ** 2.0 - i) ** 2.0)
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class Quadratic(Benchmark):
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r"""
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Quadratic objective function.
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This class defines the Quadratic [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{Quadratic}}(x) = -3803.84 - 138.08x_1 - 232.92x_2 + 128.08x_1^2
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+ 203.64x_2^2 + 182.25x_1x_2
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Here, :math:`n` represents the number of dimensions and
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:math:`x_i \in [-10, 10]` for :math:`i = 1, 2`.
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*Global optimum*: :math:`f(x) = -3873.72418` for
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:math:`x = [0.19388, 0.48513]`
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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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"""
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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([-10.0] * self.N, [10.0] * self.N))
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self.custom_bounds = [(0, 1), (0, 1)]
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self.global_optimum = [[0.19388, 0.48513]]
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self.fglob = -3873.72418
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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 (-3803.84 - 138.08 * x[0] - 232.92 * x[1] + 128.08 * x[0] ** 2.0
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+ 203.64 * x[1] ** 2.0 + 182.25 * x[0] * x[1])
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class Quintic(Benchmark):
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r"""
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Quintic objective function.
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This class defines the Quintic [1]_ global optimization problem. This is a
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multimodal minimization problem defined as follows:
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.. math::
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f_{\text{Quintic}}(x) = \sum_{i=1}^{n} \left|{x_{i}^{5} - 3 x_{i}^{4}
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+ 4 x_{i}^{3} + 2 x_{i}^{2} - 10 x_{i} -4}\right|
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Here, :math:`n` represents the number of dimensions and
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:math:`x_i \in [-10, 10]` for :math:`i = 1, ..., n`.
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*Global optimum*: :math:`f(x_i) = 0` for :math:`x_i = -1` for
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:math:`i = 1, ..., n`
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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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"""
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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([-10.0] * self.N, [10.0] * self.N))
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self.custom_bounds = [(-2, 2), (-2, 2)]
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self.global_optimum = [[-1.0 for _ in range(self.N)]]
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self.fglob = 0
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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(abs(x ** 5 - 3 * x ** 4 + 4 * x ** 3 + 2 * x ** 2
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- 10 * x - 4))
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