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Python Implementation of Perm 0,d beta Function

Updated: Jul 18, 2021




Mathematical Definition



Input Domain


It can be defined into any input domain but usually perm 0, d, beta function evaluated on the hypercube ๐‘ฅ๐‘– ๐œ– [โˆ’๐‘‘, ๐‘‘], for all ๐‘– = 1, โ€ฆ . , ๐‘‘.


Global Minima


The function has one global minimum ๐‘“(๐‘ฅ โˆ—) = 0, ๐‘Ž๐‘ก ๐‘ฅ โˆ— = (1, 1 /2 , โ€ฆ , 1 /๐‘‘ )


Description and Features


The function is defined on 2- dimensional space


Python Implementation

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import matplotlib.pyplot as plt
import numpy as np
from numpy import sin

from numpy import e
from numpy import meshgrid
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm

def f(x1,x2):
 
 return (11*(x1-1)+12*(x2-0.5))**2 + (11*(x1**2-1)+12*(x2**2-0.25))**2

x1=np.linspace(-2,2)
x2=np.linspace(-2,2)
r_min,r_max=1,2

x1,x2=np.meshgrid(x1,x2)
results=f(x1,x2)

figure=plt.figure(figsize=(9,9))
axis=figure.gca(projection='3d')
axis.contour3D(x1, x2, results,450)
axis.set_title('Perm function 0,d,beta')
axis.view_init(40,40)
axis.set_xlabel('X')
axis.set_ylabel('Y')
axis.set_zlabel('Z')
plt.show()




References:


[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.




#optimization #benchmarkfunction

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