Python Implementation of SCHAFFER FUNCTION
Updated: Jul 18, 2021
The function is defined on input domain i.e. x ∈ [−100, 100] and y ∈ [−100, 100].
The function has one global minimum f(z) = 0 at z = (0, 0).
This function is unimodal.
The function is continuous.
The function is not convex.
The function is differentiable.
The function is non-separable.
The function is defined on 2-dimensional space.
% 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 firstname.lastname@example.org % Author: Yamini Jain import matplotlib.pyplot as plt import numpy as np from matplotlib import cm def f(x,y): # Defines the function num = (np.sin((x**2 + y**2)**2)**2) - 0.5 den = (1 + 0.001*(x**2 + y**2))**2 return 0.5 + num/den X = np.linspace(-50,50) Y = np.linspace(-50,50) x,y = np.meshgrid(X,Y) # Makes a rough mesh in which graph will be plotted F = f(x,y) fig = plt.figure(figsize=(9,9)) ax = plt.axes(projection='3d') graph = ax.contour3D(x,y, F,450,cmap = cm.jet) # There are many color options to choose from # colourmaps like jet, rainbow, cube_helix and many more ax.set_title('SCHAFFER N.1 FUNCTION') #Title of the graph fig.colorbar(graph, shrink=0.5, aspect=8) #Gives a color bar ax.set_xlabel('X') #Labling axes ax.set_ylabel('Y') ax.set_zlabel('F') ax.set_xlim(50,-50) #Setting axes limit ax.set_ylim(50,-50) ax.view_init(4,4) # Viewing angle of graph plt.show()
 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.