Bartels Conn Function

Mathematical Definition

Input Domain

The function can be defined on any input domain but it is usually evaluated on x ∈ [−500,500], and y ∈ [−500,500].

Global Minima

The global minima f(x∗) =1 is located at x∗ = (0, 0).

Characteristics

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: SHIVANGI CHANDRA DUBEY
 
 #For n=2
 #bartelsConn accepts the values of 2 MxM dimension matrices X, Y
 #it returns the computation of the matrices in an MxM matrix Z
 #the function is then plotted using (X,Y,Z)
 #thus giving us a contour plot
 
 from mpl_toolkits import mplot3d
 %matplotlib inline
 import numpy as np
 import matplotlib.pyplot as plt
 from matplotlib import cm
 
 def bartelsConn(x,y):
  return abs(x**2+y**2+x*y)+abs(np.sin(x))+abs(np.cos(y))
 
 x=np.linspace(-500,500,1000)
 y=np.linspace(-500,500,1000)
 
 X,Y=np.meshgrid(x,y)
 Z=bartelsConn(X,Y)
 
 def plotFunction(e,a):
  fig=plt.figure(figsize=[12,8])
  ax=plt.axes(projection='3d')
  surf=ax.plot_surface(X,Y,Z,cmap=cm.coolwarm)
  ax.view_init(elev=e,azim=a)
  ax.set_xlabel('X')
  ax.set_ylabel('Y')
  ax.set_zlabel('fx')
  ax.set_title('Bartels Conn Function')
  fig.colorbar(surf, shrink=0.5, aspect=5)
  plt.show()
  plt.contour(X,Y,Z)
  plt.show()
 
 from ipywidgets import interactive
 iplot=interactive(plotFunction,
  e=(-90,90,5),
  a=(-90,90,5))
 
 iplot

References:

[1] Survajonic, Sonja & Bingham, Derek, “Virtual Library of Simulation Experiments”, sfu.ca,

https://www.sfu.ca/~ssurjano/optimization.html

#optimization #benchmarkfunction