top of page

Python Implementation of KEANE FUNCTION

Updated: Jul 19, 2021




Mathematical Definition


Input Domain

The Keane Function is defined on input range x [0,10] and y [0,10].


Global Minima

The Keane Function has two global minimum f(x*) = 0.673667521146855 at

  • x* = (1.393249070031784, 0)

  • x* = (0, 1.393249070031784)


Description and Features


The Keane Function is defined on 2-dimensional space. This function is considered as standard benchmark for non-linear constrained optimization.


The Keane Function is

  • Non-separable

  • Continuous

  • Differentiable

  • Non-convex

  • Multi-modal


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: RIYA SHIVHARE

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

def f(x1,x2):
        a=-sin(x1-x2)**2*sin(x1+x2)**2
        b=sqrt(x1*x1+x2*x2)   
        c=a/b
        return c 
 
x1 = np.linspace(10,-10)
x2 = np.linspace(10,-10)
x1,x2=np.meshgrid(x1,x2)
F=f(x1,x2)
fig =plt.figure(figsize=(9,9))
ax=fig.gca(projection='3d')
ax.contour3D(x1,x2,F,450)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Keane Function')
ax.view_init(21,45)

#plt.contour(x1,x2,F,15)
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

118 views0 comments
bottom of page