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# Python Implementation of LEVI N. 13 FUNCTION

Updated: Jul 19, 2021   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:

• Convergence rate

• Precision

• Robustness

• General Performance.

The Levi N.13 Function is a

• Non-separable

• Continuous

• Multi-modal

• Differentiable

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:

 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.