108 lines
3.5 KiB
Python
108 lines
3.5 KiB
Python
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# -*- coding: utf-8 -*-
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from numpy import sum, asarray, arange, exp
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from .go_benchmark import Benchmark
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class JennrichSampson(Benchmark):
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r"""
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Jennrich-Sampson objective function.
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This class defines the Jennrich-Sampson [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{JennrichSampson}}(x) = \sum_{i=1}^{10} \left [2 + 2i
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- (e^{ix_1} + e^{ix_2}) \right ]^2
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with :math:`x_i \in [-1, 1]` for :math:`i = 1, 2`.
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*Global optimum*: :math:`f(x) = 124.3621824` for
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:math:`x = [0.257825, 0.257825]`.
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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([-1.0] * self.N, [1.0] * self.N))
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self.global_optimum = [[0.257825, 0.257825]]
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self.custom_bounds = [(-1, 0.34), (-1, 0.34)]
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self.fglob = 124.3621824
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def fun(self, x, *args):
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self.nfev += 1
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i = arange(1, 11)
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return sum((2 + 2 * i - (exp(i * x[0]) + exp(i * x[1]))) ** 2)
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class Judge(Benchmark):
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r"""
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Judge objective function.
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This class defines the Judge [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{Judge}}(x) = \sum_{i=1}^{20}
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\left [ \left (x_1 + A_i x_2 + B x_2^2 \right ) - C_i \right ]^2
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Where, in this exercise:
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.. math::
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\begin{cases}
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C = [4.284, 4.149, 3.877, 0.533, 2.211, 2.389, 2.145,
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3.231, 1.998, 1.379, 2.106, 1.428, 1.011, 2.179, 2.858, 1.388, 1.651,
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1.593, 1.046, 2.152] \\
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A = [0.286, 0.973, 0.384, 0.276, 0.973, 0.543, 0.957, 0.948, 0.543,
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0.797, 0.936, 0.889, 0.006, 0.828, 0.399, 0.617, 0.939, 0.784,
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0.072, 0.889] \\
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B = [0.645, 0.585, 0.310, 0.058, 0.455, 0.779, 0.259, 0.202, 0.028,
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0.099, 0.142, 0.296, 0.175, 0.180, 0.842, 0.039, 0.103, 0.620,
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0.158, 0.704]
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\end{cases}
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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_i) = 16.0817307` for
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:math:`\mathbf{x} = [0.86479, 1.2357]`.
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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 = [[0.86479, 1.2357]]
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self.custom_bounds = [(-2.0, 2.0), (-2.0, 2.0)]
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self.fglob = 16.0817307
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self.c = asarray([4.284, 4.149, 3.877, 0.533, 2.211, 2.389, 2.145,
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3.231, 1.998, 1.379, 2.106, 1.428, 1.011, 2.179,
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2.858, 1.388, 1.651, 1.593, 1.046, 2.152])
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self.a = asarray([0.286, 0.973, 0.384, 0.276, 0.973, 0.543, 0.957,
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0.948, 0.543, 0.797, 0.936, 0.889, 0.006, 0.828,
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0.399, 0.617, 0.939, 0.784, 0.072, 0.889])
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self.b = asarray([0.645, 0.585, 0.310, 0.058, 0.455, 0.779, 0.259,
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0.202, 0.028, 0.099, 0.142, 0.296, 0.175, 0.180,
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0.842, 0.039, 0.103, 0.620, 0.158, 0.704])
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def fun(self, x, *args):
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self.nfev += 1
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return sum(((x[0] + x[1] * self.a + (x[1] ** 2.0) * self.b) - self.c)
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** 2.0)
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