PERIODIC FUNCTION

Mathematical Definition

Input Domain

The Periodic Function is defined on input range xi [-10,10] for i=1…n

Global Minima

The Periodic Function has on global minimum f(x*)=0.9 at x*=(0…0).

Description and Features

The Periodic Function is a function that repeats its values at regular intervals. This function is defined on n-dimensional space and used to describe oscillations, waves and other phenomena that exhibit periodicity.

The Periodic Function is a

Python Implementation

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 import matplotlib.pyplot as plt
 import numpy as np
 from numpy import sin
 from numpy import exp
 from mpl_toolkits import mplot3d
 def f(x1,x2):
  return 1+ sin(x1)**2 + sin(x2)**2-0.1*exp(-x1*x1-x2*x2)
 
 x1=np.linspace(-2,2)
 x2=np.linspace(-2,2)
 x1,x2=np.meshgrid(x1,x2)
 
 results=f(x1,x2)
 fig =plt.figure(figsize=(9,9))
 
 axis=fig.gca(projection='3d')
 axis.contour3D(x1,x2,results,450)
 axis.set_xlabel('X')
 axis.set_ylabel('Y')
 axis.set_zlabel('Z')
 axis.set_title('Periodic Function')
 axis.view_init(21,45)
 
 #plt.contour(x1,x2,results,15)
 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.

#optimization #benchmarkfunction