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SALOMON FUNCTION




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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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


#optimization #benchmarkfunction

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