45 lines
1.3 KiB
Python
45 lines
1.3 KiB
Python
# -*- coding: utf-8 -*-
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from .go_benchmark import Benchmark
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class FreudensteinRoth(Benchmark):
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r"""
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FreudensteinRoth objective function.
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This class defines the Freudenstein & Roth [1]_ global optimization problem.
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This is a multimodal minimization problem defined as follows:
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.. math::
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f_{\text{FreudensteinRoth}}(x) = \left\{x_1 - 13 + \left[(5 - x_2) x_2
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- 2 \right] x_2 \right\}^2 + \left \{x_1 - 29
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+ \left[(x_2 + 1) x_2 - 14 \right] x_2 \right\}^2
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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` for :math:`x = [5, 4]`
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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([-10.0] * self.N, [10.0] * self.N))
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self.custom_bounds = [(-3, 3), (-5, 5)]
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self.global_optimum = [[5.0, 4.0]]
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self.fglob = 0.0
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def fun(self, x, *args):
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self.nfev += 1
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f1 = (-13.0 + x[0] + ((5.0 - x[1]) * x[1] - 2.0) * x[1]) ** 2
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f2 = (-29.0 + x[0] + ((x[1] + 1.0) * x[1] - 14.0) * x[1]) ** 2
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return f1 + f2
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