Mathematical Definition
Input Domain
The function can be defined on any input domain but it is usually evaluated on x ∈ [−32, 32] and y ∈ [−32, 32].
Global Minima
The global minimum of the function is at f(x∗ ) = −200 located at x ∗ = (0, 0).
Description and Features
The function is convex.
The function is defined on 2-dimensional space.
The function is non-separable.
The function is differentiable.
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: Yamini Jain
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
import numpy as np
def f(x,y):
return -200*np.exp(-0.2*np.sqrt(x**2 + y**2))
X = np.linspace(-32,32)
Y = np.linspace(-32,32)
x,y = np.meshgrid(X,Y)
F = f(x,y)
fig = plt.figure(figsize=(9,9))
ax = plt.axes(projection='3d')
ax.contour3D(x,y, F,450)
ax.set_title('Plot Ques 2')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('F')
ax.view_init(21,45)
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.
Comments