# -*- coding: utf-8 -*- from numpy import abs, sum, sign, arange from .go_benchmark import Benchmark class Zacharov(Benchmark): r""" Zacharov objective function. This class defines the Zacharov [1]_ global optimization problem. This is a multimodal minimization problem defined as follows: .. math:: f_{\text{Zacharov}}(x) = \sum_{i=1}^{n} x_i^2 + \left ( \frac{1}{2} \sum_{i=1}^{n} i x_i \right )^2 + \left ( \frac{1}{2} \sum_{i=1}^{n} i x_i \right )^4 Here, :math:`n` represents the number of dimensions and :math:`x_i \in [-5, 10]` for :math:`i = 1, ..., n`. *Global optimum*: :math:`f(x) = 0` for :math:`x_i = 0` for :math:`i = 1, ..., n` .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194. """ def __init__(self, dimensions=2): Benchmark.__init__(self, dimensions) self._bounds = list(zip([-5.0] * self.N, [10.0] * self.N)) self.custom_bounds = ([-1, 1], [-1, 1]) self.global_optimum = [[0 for _ in range(self.N)]] self.fglob = 0.0 self.change_dimensionality = True def fun(self, x, *args): self.nfev += 1 u = sum(x ** 2) v = sum(arange(1, self.N + 1) * x) return u + (0.5 * v) ** 2 + (0.5 * v) ** 4 class ZeroSum(Benchmark): r""" ZeroSum objective function. This class defines the ZeroSum [1]_ global optimization problem. This is a multimodal minimization problem defined as follows: .. math:: f_{\text{ZeroSum}}(x) = \begin{cases} 0 & \textrm{if} \sum_{i=1}^n x_i = 0 \\ 1 + \left(10000 \left |\sum_{i=1}^n x_i\right| \right)^{0.5} & \textrm{otherwise} \end{cases} Here, :math:`n` represents the number of dimensions and :math:`x_i \in [-10, 10]` for :math:`i = 1, ..., n`. *Global optimum*: :math:`f(x) = 0` where :math:`\sum_{i=1}^n x_i = 0` .. [1] Gavana, A. Global Optimization Benchmarks and AMPGO retrieved 2015 """ def __init__(self, dimensions=2): Benchmark.__init__(self, dimensions) self._bounds = list(zip([-10.0] * self.N, [10.0] * self.N)) self.global_optimum = [[]] self.fglob = 0.0 self.change_dimensionality = True def fun(self, x, *args): self.nfev += 1 if abs(sum(x)) < 3e-16: return 0.0 return 1.0 + (10000.0 * abs(sum(x))) ** 0.5 class Zettl(Benchmark): r""" Zettl objective function. This class defines the Zettl [1]_ global optimization problem. This is a multimodal minimization problem defined as follows: .. math:: f_{\text{Zettl}}(x) = \frac{1}{4} x_{1} + \left(x_{1}^{2} - 2 x_{1} + x_{2}^{2}\right)^{2} with :math:`x_i \in [-1, 5]` for :math:`i = 1, 2`. *Global optimum*: :math:`f(x) = -0.0037912` for :math:`x = [-0.029896, 0.0]` .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194. """ def __init__(self, dimensions=2): Benchmark.__init__(self, dimensions) self._bounds = list(zip([-5.0] * self.N, [10.0] * self.N)) self.global_optimum = [[-0.02989597760285287, 0.0]] self.fglob = -0.003791237220468656 def fun(self, x, *args): self.nfev += 1 return (x[0] ** 2 + x[1] ** 2 - 2 * x[0]) ** 2 + 0.25 * x[0] class Zimmerman(Benchmark): r""" Zimmerman objective function. This class defines the Zimmerman [1]_ global optimization problem. This is a multimodal minimization problem defined as follows: .. math:: f_{\text{Zimmerman}}(x) = \max \left[Zh1(x), Zp(Zh2(x)) \textrm{sgn}(Zh2(x)), Zp(Zh3(x)) \textrm{sgn}(Zh3(x)), Zp(-x_1)\textrm{sgn}(x_1), Zp(-x_2)\textrm{sgn}(x_2) \right] Where, in this exercise: .. math:: \begin{cases} Zh1(x) = 9 - x_1 - x_2 \\ Zh2(x) = (x_1 - 3)^2 + (x_2 - 2)^2 \\ Zh3(x) = x_1x_2 - 14 \\ Zp(t) = 100(1 + t) \end{cases} Where :math:`x` is a vector and :math:`t` is a scalar. Here, :math:`x_i \in [0, 100]` for :math:`i = 1, 2`. *Global optimum*: :math:`f(x) = 0` for :math:`x = [7, 2]` .. [1] Gavana, A. Global Optimization Benchmarks and AMPGO retrieved 2015 TODO implementation from Gavana """ def __init__(self, dimensions=2): Benchmark.__init__(self, dimensions) self._bounds = list(zip([0.0] * self.N, [100.0] * self.N)) self.custom_bounds = ([0.0, 8.0], [0.0, 8.0]) self.global_optimum = [[7.0, 2.0]] self.fglob = 0.0 def fun(self, x, *args): self.nfev += 1 Zh1 = lambda x: 9.0 - x[0] - x[1] Zh2 = lambda x: (x[0] - 3.0) ** 2.0 + (x[1] - 2.0) ** 2.0 - 16.0 Zh3 = lambda x: x[0] * x[1] - 14.0 Zp = lambda x: 100.0 * (1.0 + x) return max(Zh1(x), Zp(Zh2(x)) * sign(Zh2(x)), Zp(Zh3(x)) * sign(Zh3(x)), Zp(-x[0]) * sign(x[0]), Zp(-x[1]) * sign(x[1])) class Zirilli(Benchmark): r""" Zettl objective function. This class defines the Zirilli [1]_ global optimization problem. This is a unimodal minimization problem defined as follows: .. math:: f_{\text{Zirilli}}(x) = 0.25x_1^4 - 0.5x_1^2 + 0.1x_1 + 0.5x_2^2 Here, :math:`n` represents the number of dimensions and :math:`x_i \in [-10, 10]` for :math:`i = 1, 2`. *Global optimum*: :math:`f(x) = -0.3523` for :math:`x = [-1.0465, 0]` .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions For Global Optimization Problems Int. Journal of Mathematical Modelling and Numerical Optimisation, 2013, 4, 150-194. """ def __init__(self, dimensions=2): Benchmark.__init__(self, dimensions) self._bounds = list(zip([-10.0] * self.N, [10.0] * self.N)) self.custom_bounds = ([-2.0, 2.0], [-2.0, 2.0]) self.global_optimum = [[-1.0465, 0.0]] self.fglob = -0.35238603 def fun(self, x, *args): self.nfev += 1 return 0.25 * x[0] ** 4 - 0.5 * x[0] ** 2 + 0.1 * x[0] + 0.5 * x[1] ** 2