150 lines
4.5 KiB
Python
150 lines
4.5 KiB
Python
# -*- coding: utf-8 -*-
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from numpy import asarray, atleast_2d, arange, sin, sqrt, prod, sum, round
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from .go_benchmark import Benchmark
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class Katsuura(Benchmark):
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r"""
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Katsuura objective function.
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This class defines the Katsuura [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{Katsuura}}(x) = \prod_{i=0}^{n-1} \left [ 1 +
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(i+1) \sum_{k=1}^{d} \lfloor (2^k x_i) \rfloor 2^{-k} \right ]
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Where, in this exercise, :math:`d = 32`.
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Here, :math:`n` represents the number of dimensions and
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:math:`x_i \in [0, 100]` 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] Adorio, E. MVF - "Multivariate Test Functions Library in C for
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Unconstrained Global Optimization", 2005
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.. [2] Gavana, A. Global Optimization Benchmarks and AMPGO retrieved 2015
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TODO: Adorio has wrong global minimum. Adorio uses round, Gavana docstring
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uses floor, but Gavana code uses round. We'll use round...
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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([0.0] * self.N, [100.0] * self.N))
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self.global_optimum = [[0.0 for _ in range(self.N)]]
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self.custom_bounds = [(0, 1), (0, 1)]
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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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d = 32
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k = atleast_2d(arange(1, d + 1)).T
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i = arange(0., self.N * 1.)
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inner = round(2 ** k * x) * (2. ** (-k))
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return prod(sum(inner, axis=0) * (i + 1) + 1)
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class Keane(Benchmark):
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r"""
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Keane objective function.
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This class defines the Keane [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{Keane}}(x) = \frac{\sin^2(x_1 - x_2)\sin^2(x_1 + x_2)}
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{\sqrt{x_1^2 + x_2^2}}
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with :math:`x_i \in [0, 10]` for :math:`i = 1, 2`.
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*Global optimum*: :math:`f(x) = 0.0` for
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:math:`x = [7.85396153, 7.85396135]`.
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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 #69, there is no way that the function can have a negative
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value. Everything is squared. I think that they have the wrong solution.
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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([0.0] * self.N, [10.0] * self.N))
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self.global_optimum = [[7.85396153, 7.85396135]]
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self.custom_bounds = [(-1, 0.34), (-1, 0.34)]
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self.fglob = 0.
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def fun(self, x, *args):
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self.nfev += 1
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val = sin(x[0] - x[1]) ** 2 * sin(x[0] + x[1]) ** 2
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return val / sqrt(x[0] ** 2 + x[1] ** 2)
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class Kowalik(Benchmark):
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r"""
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Kowalik objective function.
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This class defines the Kowalik [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{Kowalik}}(x) = \sum_{i=0}^{10} \left [ a_i
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- \frac{x_1 (b_i^2 + b_i x_2)} {b_i^2 + b_i x_3 + x_4} \right ]^2
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Where:
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.. math::
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\begin{matrix}
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a = [4, 2, 1, 1/2, 1/4 1/8, 1/10, 1/12, 1/14, 1/16] \\
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b = [0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
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0.0456, 0.0342, 0.0323, 0.0235, 0.0246]\\
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\end{matrix}
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Here, :math:`n` represents the number of dimensions and :math:`x_i \in
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[-5, 5]` for :math:`i = 1, ..., 4`.
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*Global optimum*: :math:`f(x) = 0.00030748610` for :math:`x =
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[0.192833, 0.190836, 0.123117, 0.135766]`.
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..[1] https://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml
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"""
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def __init__(self, dimensions=4):
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Benchmark.__init__(self, dimensions)
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self._bounds = list(zip([-5.0] * self.N, [5.0] * self.N))
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self.global_optimum = [[0.192833, 0.190836, 0.123117, 0.135766]]
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self.fglob = 0.00030748610
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self.a = asarray([4.0, 2.0, 1.0, 1 / 2.0, 1 / 4.0, 1 / 6.0, 1 / 8.0,
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1 / 10.0, 1 / 12.0, 1 / 14.0, 1 / 16.0])
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self.b = asarray([0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
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0.0456, 0.0342, 0.0323, 0.0235, 0.0246])
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def fun(self, x, *args):
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self.nfev += 1
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vec = self.b - (x[0] * (self.a ** 2 + self.a * x[1])
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/ (self.a ** 2 + self.a * x[2] + x[3]))
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return sum(vec ** 2)
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