150 lines
4.0 KiB
Python
150 lines
4.0 KiB
Python
# -*- coding: utf-8 -*-
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from numpy import cos, sqrt, sin, abs
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from .go_benchmark import Benchmark
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class NeedleEye(Benchmark):
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r"""
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NeedleEye objective function.
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This class defines the Needle-Eye [1]_ global optimization problem. This is a
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a multimodal minimization problem defined as follows:
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.. math::
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f_{\text{NeedleEye}}(x) =
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\begin{cases}
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1 & \textrm{if }\hspace{5pt} \lvert x_i \rvert < eye \hspace{5pt}
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\forall i \\
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\sum_{i=1}^n (100 + \lvert x_i \rvert) & \textrm{if } \hspace{5pt}
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\lvert x_i \rvert > eye \\
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0 & \textrm{otherwise}\\
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\end{cases}
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Where, in this exercise, :math:`eye = 0.0001`.
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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) = 1` for :math:`x_i = 0` for
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: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([-10.0] * self.N, [10.0] * self.N))
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self.global_optimum = [[0.0 for _ in range(self.N)]]
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self.fglob = 1.0
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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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f = fp = 0.0
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eye = 0.0001
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for val in x:
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if abs(val) >= eye:
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fp = 1.0
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f += 100.0 + abs(val)
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else:
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f += 1.0
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if fp < 1e-6:
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f = f / self.N
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return f
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class NewFunction01(Benchmark):
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r"""
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NewFunction01 objective function.
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This class defines the NewFunction01 [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{NewFunction01}}(x) = \left | {\cos\left(\sqrt{\left|{x_{1}^{2}
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+ x_{2}}\right|}\right)} \right |^{0.5} + (x_{1} + x_{2})/100
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with :math:`x_i \in [-10, 10]` for :math:`i = 1, 2`.
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*Global optimum*: :math:`f(x) = -0.18459899925` for
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:math:`x = [-8.46669057, -9.99982177]`
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.. [1] Mishra, S. Global Optimization by Differential Evolution and
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Particle Swarm Methods: Evaluation on Some Benchmark Functions.
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Munich Personal RePEc Archive, 2006, 1005
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TODO line 355
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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.global_optimum = [[-8.46668984648, -9.99980944557]]
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self.fglob = -0.184648852475
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def fun(self, x, *args):
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self.nfev += 1
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return ((abs(cos(sqrt(abs(x[0] ** 2 + x[1]))))) ** 0.5
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+ 0.01 * (x[0] + x[1]))
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class NewFunction02(Benchmark):
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r"""
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NewFunction02 objective function.
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This class defines the NewFunction02 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{NewFunction02}}(x) = \left | {\sin\left(\sqrt{\lvert{x_{1}^{2}
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+ x_{2}}\rvert}\right)} \right |^{0.5} + (x_{1} + x_{2})/100
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with :math:`x_i \in [-10, 10]` for :math:`i = 1, 2`.
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*Global optimum*: :math:`f(x) = -0.19933159253` for
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:math:`x = [-9.94103375, -9.99771235]`
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.. [1] Mishra, S. Global Optimization by Differential Evolution and
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Particle Swarm Methods: Evaluation on Some Benchmark Functions.
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Munich Personal RePEc Archive, 2006, 1005
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TODO Line 368
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TODO WARNING, minimum value is estimated from running many optimisations and
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choosing the best.
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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.global_optimum = [[-9.94114736324, -9.99997128772]]
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self.fglob = -0.199409030092
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def fun(self, x, *args):
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self.nfev += 1
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return ((abs(sin(sqrt(abs(x[0] ** 2 + x[1]))))) ** 0.5
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+ 0.01 * (x[0] + x[1]))
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#Newfunction 3 from Gavana is entered as Mishra05.
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