Mathematical Definition
Input Domain
It can be defined on any input domain but it’s usually evaluated on the square 𝑥𝑖 ∈ [−100,100] for i=1,2
Global Minima
It has one local minima at 𝑓(𝑥 ∗ ) = 0 𝑎𝑡 𝑥 ∗ = (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
% Please forward any comments or bug reports in chat
Copyright 2021. INDUSMIC PRIVATE LIMITED.THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY FOR THE USE OF THIS PROGRAM. If software is modified to produce derivative works, such modified software should be clearly marked. Additionally, user can redistribute it and/or modify it under the terms of the GNU General Public License. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY. See the GNU General Public License for more details.
% for any support connect with us on help.indusmic@gmail.com
% Author: Ekta Kumari
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.
Comments