Updated: Jul 18, 2021
The function can be defined on any input domain but it is usually evaluated on xi∈[−500,500] for i=1,…,n. Here, n = 2.
The global minima f(x*)=0 are located at x*=(±√i,…,±√i)
Description and Features
The function is continuous, not convex, defined on n-dimensional space, multimodal, differentiable, non-separable.
% Please forward any comments or bug reports in chat Copyright 2021. INDUSMIC PRIVATE LIMITED. THERE IS NO WARRANTY, EXPRESSOR 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: Sakshi Chadda import numpy as np import matplotlib.pyplot as plt fig = plt.figure() ax = fig.gca(projection='3d') x = np.arange(-500, 500, 0.1) y = np.arange(-500, 500, 0.1) x, y = np.meshgrid(x, y) res = 0 for i in range(3): res = res + ((x ** 2 + y ** 2) -i) ** 2 ax.plot_surface(x, y, res, cmap='jet') plt.show() plt.contour(x,y,res) 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.