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SHUBERT 3 FUNCTION





Mathematical Definition


Input Domain


The function can be defined on any input domain but it is usually evaluated on xi ∈[−10,10] for i=1,…,n. Here, n = 2.


Global Minima


The function has one global minimum f(x*)=−29.6733337.


Characteristics


The function is continuous, not convex, defined on n-dimensional space, multimodal, differentiable, separable.


Python Implementation


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import numpy as np
from numpy import sin
import matplotlib.pyplot as plt
 fig = plt.figure()
 ax = fig.gca(projection='3d')
 x = np.arange(-10, 10, 0.1)
 y = np.arange(-10, 10,0.1)
 x, y = np.meshgrid(x, y)
 n = int(input("enter number N :"))
 sum = 0
for i in range(1, n+1):
 for j in range(1,6):
 sum = sum + (j * sin((j + 1) * x + y + j))
 surface = ax.plot_surface(x, y, sum, cmap='Purples')
 plt.show()
 plt.contour(x,y,sum)
 plt.show()
 plt.scatter(x, y, sum)
 plt.show()

References:


[1] Survajonic, Sonja & Bingham, Derek, “Virtual Library of Simulation Experiments”, sfu.ca,

https://www.sfu.ca/~ssurjano/optimization.html


#optimization #benchmarkfunction

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