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Shubert Function

Updated: Jul 18, 2021

Mathematical Definition

Input Domain

It can define into any input domain but usually its evaluated on the square ๐‘ฅ๐‘– โˆˆ [โˆ’10,10] for all i= 1,2

Global Minima

It has 18 global minima ๐‘“(๐‘ฅ โˆ— ) โ‰ˆ โˆ’186.7309.

Description and Features

Shubert function is continuous function.

The function is differentiable.

The function is non-separable.

The function is defined on n โ€“ dimensional space.

Python Implementation

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import matplotlib.pyplot as plt
import numpy as np
from numpy import sin
from numpy import *
from numpy import pi
from numpy import sqrt
from matplotlib import cm

def f(x1,x2):
      for i in range(1,6):
          sum1 = sum1 + (i* cos(((i+1)*x1) +i))
          sum2 = sum2 + (i* cos(((i+1)*x2) +i))
      return sum1 * sum2
x1 =np.linspace(-10,10,100)
x2 =np.linspace(-10,10,100)
r_min,r_max= -10,10


axis.contour3D(x1, x2, results,15)
axis.set_title('Shubert function')
axis.plot_surface(x1,x2,results, cmap=cm.rainbow)

plt.contour(x1, x2, results,15)


[1] Jamil, Momin, and Xin-She Yang. "A literature survey of benchmark functions for global optimization problems." International Journal of Mathematical Modelling and Numerical Optimization 4.2 (2013): 150-194.

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