top of page
Music Apps
Writer's pictureIndusmic Private Limited

BUKIN FUNCTION N.6

Updated: Aug 5, 2021




Mathematical Definition


Input Domain


The function is evaluated on the rectangle x1∈[−15,−5] and x2∈[−3,3] but it can be

defined on any input domain.


Global Minima


The function has one global minimum f(x0)=0 at x0=f(−10,1).


Description and Features


Dimension: 2

The Bukin function N.6 has many local minima, all of which lie in a ridge.


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: Parakh Jain 

import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
import numpy as np

def f(x1,x2):
    ab=np.fabs(x2-0.01*x1*x1)
    a=100*np.sqrt(ab)+0.01*np.fabs(x1+10)
    return a
x1=np.linspace(-15,-5)
x2=np.linspace(-3,3)
X1,X2=np.meshgrid(x1,x2)

def plotter(E,A):
    fig=plt.figure(figsize=[12,8])
    ax=plt.axes(projection='3d')
    ax.plot_surface(X1,X2,f(X1,X2),color='purple',alpha=0.7)
    ax.plot_wireframe(X1,X2,f(X1,X2),ccount=5,rcount=10,color='red', alpha=0.8)
    ax.view_init(elev=E,azim=A)
    ax.set_xlabel('x1')
    ax.set_ylabel('x2')
    ax.set_zlabel('f(x1,x2)')
    ax.set_title('f(x1,x2)=100*sqrt(fabs(x2-0.01*x1*x1)) +0.01*fabs(x1+10)')
    plt.show()

from ipywidgets import interactive
iplot=interactive(plotter,E=(-90,90,5),A=(-90,90,5))
iplot




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.




955 views0 comments

Comments


bottom of page