Python Implementation of LEVI N. 13 FUNCTION

Mathematical Definition

Input Domain

The Levi N. 13 Function is defined on input range x [-10,10] and y [-10,10].

Global Minima

The Levi N. 13 Function has one global minimum f(x*)=0 at x* = (1,1)

Description and Features

The Levi N. 13 Function is defined on two dimensional space. This function is used as a test function to evaluate the performance of optimization algorithms such as:

The Levi N.13 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 pi
 from mpl_toolkits import mplot3d
 
 def f(x,y):
  a= sin(3*pi*x)**2 + (x-1)**2*(1+sin(3*pi*y)*sin(3*pi*y))+ (y-1)*(y-1)*(1+sin(2*pi*y)*sin(2*pi*y))
  return a
 
 x=np.linspace(-10,10)
 y=np.linspace(-10,10)
 
 x,y=np.meshgrid(x,y)
 F=f(x,y)
 
 fig =plt.figure(figsize=(9,9))
 ax=fig.gca(projection='3d')
 ax.contour3D(x,y,F,450)
 
 ax.set_xlabel('X')
 ax.set_ylabel('Y')
 ax.set_zlabel('Z')
 ax.set_title('Levi N.13 Function')
 ax.view_init(21,45)
 
 #plt.contour(x,y,F,30)
 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