top of page
Search

# Python Implementation of LEON FUNCTION   Leon Function is a multimodal minimization problem, Continuous function having a single global minima defined on n- dimensional space.

Mathematical Definition Input Domain

The input range for Leon function is -1.2 ≤xi≤ 1.2 where i= 1,2, (0 ≤ x ≤ 10), (0 ≤ y ≤ 10). This function is smooth.

Global Minima

Leon function has a single global minimum located at f (x ∗) = f(1, 1), f(x ∗ ) = 0.

Description and Features

• Continuous Function

• Differentiable Function

• Non- Convex

• Non- Seperable

• Multimodel Function

Python Implementation

```% Please forward any comments or bug reports in chat
Copyright 2021. INDUSMIC PRIVATE LIMITED.THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY FOR THE USE OF THIS PROGRAM. If software is modified to produce derivative works, such modified software should be clearly marked. Additionally, user can redistribute it and/or modify it under the terms of the GNU General Public License. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY. See the GNU General Public License for more details.
% for any support connect with us on help.indusmic@gmail.com
% Author: Vanshita Tripathi

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from numpy import *
#from numpy import arrange

from numpy import meshgrid
from mpl_toolkits.mplot3d import Axes3D
%matplotlib notebook
plt.rcParams['figure.figsize'] = (6,4)
plt.rcParams['figure.dpi']=150
fig=plt.figure()
axis = fig.gca(projection= '3d')

def f(x,y):
return 100*(y-x**3)**2 + (1-x)**2
x= np.linspace(0,10)
y= np.linspace(0,10)
r_min, r_max= 0.0, 10.0
x,y= np.meshgrid(x,y)
results= f(x,y)
figure = plt.figure()
axis.plot_surface(x,y,results,cmap= 'jet')
axis.view_init(10,10)

```

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.