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Python Implementation of Bohachevsky Function

Updated: Jul 18, 2021







Mathematical Definition



Input Domain


It can be defined on any input domain but itโ€™s usually evaluated on the square ๐‘ฅ๐‘– โˆˆ [โˆ’100,100] for i=1,2


Global Minima


It has one local minima at ๐‘“(๐‘ฅ โˆ— ) = 0 ๐‘Ž๐‘ก ๐‘ฅ โˆ— = (0,0).


Description and Features


Bohachevsky functions are continuous.

The function is defined on 2- dimensional space.

Bohachevsky functions are unimodal.

The functions all have the same similar bowl shape



Python Implementation

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import matplotlib.pyplot as plt
import numpy as np
from numpy import *
from numpy import cos
from numpy import pi
from numpy import abs,sqrt
from numpy import meshgrid
from mpl_toolkits.mplot3d import Axes3D

def f( x1,x2):  
  return x1**2 +2*(x2**2)-0.3*cos(3*pi*x1)-0.4*cos(4*pi*x2)+0.7

x1=np.linspace(-100,100,500)
x2=np.linspace(-100,100,500)
r_min,r_max=-100,100

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('Bohachevsky function')
axis.view_init(21,40)
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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