Mathematical Definition
Input Domain
The function can be defined on any input domain but it is usually evaluated on xi ∈[−100,100] for i=1,…,n. Here, n =2.
Global Minima
The function has one global minimum f(x∗) =0 are located at x∗=(0,…,0).
Characteristics
The function is continuous, not convex, defined on n-dimensional space, multimodal, differentiable, non - separable.
Python Implementation
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% Author: Sakshi Chadda
import numpy as np
import matplotlib.pyplot as plt
from numpy import sqrt
from numpy import cos
from numpy import pi
fig = plt.figure()
ax = fig.gca(projection='3d')
x = np.arange(-100, 100)
y = np.arange(-10, 10)
x, y = np.meshgrid(x, y)
r = x**2+y**2
z = 1-cos(2 * pi * sqrt(r) + 0.1 * sqrt(r))
surface = ax.plot_surface(x, y, z, cmap='coolwarm')
plt.show()
plt.contour(x,y,z)
plt.show()
plt.scatter(x, y, z)
plt.show()References:
[1] Survajonic, Sonja & Bingham, Derek, “Virtual Library of Simulation Experiments”, sfu.ca,
https://www.sfu.ca/~ssurjano/optimization.html