167 lines
5.0 KiB
Python
167 lines
5.0 KiB
Python
# -*- coding: utf-8 -*-
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from numpy import abs, sin, cos, pi, sqrt
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from .go_benchmark import Benchmark
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class Ursem01(Benchmark):
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r"""
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Ursem 1 objective function.
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This class defines the Ursem 1 [1]_ global optimization problem. This is a
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unimodal minimization problem defined as follows:
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.. math::
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f_{\text{Ursem01}}(x) = - \sin(2x_1 - 0.5 \pi) - 3 \cos(x_2) - 0.5 x_1
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with :math:`x_1 \in [-2.5, 3]` and :math:`x_2 \in [-2, 2]`.
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*Global optimum*: :math:`f(x) = -4.81681406371` for
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:math:`x = [1.69714, 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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"""
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def __init__(self, dimensions=2):
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Benchmark.__init__(self, dimensions)
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self._bounds = [(-2.5, 3.0), (-2.0, 2.0)]
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self.global_optimum = [[1.69714, 0.0]]
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self.fglob = -4.81681406371
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def fun(self, x, *args):
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self.nfev += 1
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return -sin(2 * x[0] - 0.5 * pi) - 3.0 * cos(x[1]) - 0.5 * x[0]
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class Ursem03(Benchmark):
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r"""
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Ursem 3 objective function.
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This class defines the Ursem 3 [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{Ursem03}}(x) = - \sin(2.2 \pi x_1 + 0.5 \pi)
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\frac{2 - \lvert x_1 \rvert}{2}
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\frac{3 - \lvert x_1 \rvert}{2}
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- \sin(2.2 \pi x_2 + 0.5 \pi)
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\frac{2 - \lvert x_2 \rvert}{2}
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\frac{3 - \lvert x_2 \rvert}{2}
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with :math:`x_1 \in [-2, 2]`, :math:`x_2 \in [-1.5, 1.5]`.
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*Global optimum*: :math:`f(x) = -3` for :math:`x = [0, 0]`
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.. [1] Gavana, A. Global Optimization Benchmarks and AMPGO retrieved 2015
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TODO Gavana and Jamil #157 disagree on the formulae here. Jamil squares the
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x[1] term in the sine expression. Gavana doesn't. Go with Gavana here.
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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 = [(-2, 2), (-1.5, 1.5)]
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self.global_optimum = [[0.0 for _ in range(self.N)]]
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self.fglob = -3.0
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def fun(self, x, *args):
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self.nfev += 1
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u = -(sin(2.2 * pi * x[0] + 0.5 * pi)
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* ((2.0 - abs(x[0])) / 2.0) * ((3.0 - abs(x[0])) / 2))
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v = -(sin(2.2 * pi * x[1] + 0.5 * pi)
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* ((2.0 - abs(x[1])) / 2) * ((3.0 - abs(x[1])) / 2))
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return u + v
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class Ursem04(Benchmark):
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r"""
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Ursem 4 objective function.
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This class defines the Ursem 4 [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{Ursem04}}(x) = -3 \sin(0.5 \pi x_1 + 0.5 \pi)
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\frac{2 - \sqrt{x_1^2 + x_2 ^ 2}}{4}
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with :math:`x_i \in [-2, 2]` for :math:`i = 1, 2`.
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*Global optimum*: :math:`f(x) = -1.5` for :math:`x = [0, 0]` for
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:math:`i = 1, 2`
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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([-2.0] * self.N, [2.0] * self.N))
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self.global_optimum = [[0.0 for _ in range(self.N)]]
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self.fglob = -1.5
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def fun(self, x, *args):
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self.nfev += 1
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return (-3 * sin(0.5 * pi * x[0] + 0.5 * pi)
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* (2 - sqrt(x[0] ** 2 + x[1] ** 2)) / 4)
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class UrsemWaves(Benchmark):
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r"""
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Ursem Waves objective function.
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This class defines the Ursem Waves [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{UrsemWaves}}(x) = -0.9x_1^2 + (x_2^2 - 4.5x_2^2)x_1x_2
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+ 4.7 \cos \left[ 2x_1 - x_2^2(2 + x_1)
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\right ] \sin(2.5 \pi x_1)
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with :math:`x_1 \in [-0.9, 1.2]`, :math:`x_2 \in [-1.2, 1.2]`.
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*Global optimum*: :math:`f(x) = -8.5536` for :math:`x = [1.2, 1.2]`
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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 #159, has an x_2^2 - 4.5 x_2^2 in the brackets. Why wasn't this
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rationalised to -5.5 x_2^2? This makes me wonder if the equation is listed
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correctly?
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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 = [(-0.9, 1.2), (-1.2, 1.2)]
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self.global_optimum = [[1.2 for _ in range(self.N)]]
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self.fglob = -8.5536
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def fun(self, x, *args):
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self.nfev += 1
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u = -0.9 * x[0] ** 2
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v = (x[1] ** 2 - 4.5 * x[1] ** 2) * x[0] * x[1]
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w = 4.7 * cos(3 * x[0] - x[1] ** 2 * (2 + x[0])) * sin(2.5 * pi * x[0])
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return u + v + w
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