63 lines
1.9 KiB
Python
63 lines
1.9 KiB
Python
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# -*- coding: utf-8 -*-
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from numpy import sum, cos, exp, pi, asarray
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from .go_benchmark import Benchmark
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class OddSquare(Benchmark):
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r"""
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Odd Square objective function.
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This class defines the Odd Square [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{OddSquare}}(x) = -e^{-\frac{d}{2\pi}} \cos(\pi d)
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\left( 1 + \frac{0.02h}{d + 0.01} \right )
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Where, in this exercise:
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.. math::
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\begin{cases}
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d = n \cdot \smash{\displaystyle\max_{1 \leq i \leq n}}
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\left[ (x_i - b_i)^2 \right ] \\
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h = \sum_{i=1}^{n} (x_i - b_i)^2
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\end{cases}
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And :math:`b = [1, 1.3, 0.8, -0.4, -1.3, 1.6, -0.2, -0.6, 0.5, 1.4, 1, 1.3,
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0.8, -0.4, -1.3, 1.6, -0.2, -0.6, 0.5, 1.4]`
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Here, :math:`n` represents the number of dimensions and
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:math:`x_i \in [-5 \pi, 5 \pi]` for :math:`i = 1, ..., n` and
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:math:`n \leq 20`.
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*Global optimum*: :math:`f(x_i) = -1.0084` for :math:`x \approx b`
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.. [1] Gavana, A. Global Optimization Benchmarks and AMPGO retrieved 2015
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TODO The best solution changes on dimensionality
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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([-5.0 * pi] * self.N,
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[5.0 * pi] * self.N))
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self.custom_bounds = ([-2.0, 4.0], [-2.0, 4.0])
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self.a = asarray([1, 1.3, 0.8, -0.4, -1.3, 1.6, -0.2, -0.6, 0.5, 1.4]
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* 2)
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self.global_optimum = [[1.0873320463871847, 1.3873320456818079]]
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self.fglob = -1.00846728102
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def fun(self, x, *args):
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self.nfev += 1
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b = self.a[0: self.N]
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d = self.N * max((x - b) ** 2.0)
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h = sum((x - b) ** 2.0)
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return (-exp(-d / (2.0 * pi)) * cos(pi * d)
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* (1.0 + 0.02 * h / (d + 0.01)))
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