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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



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% 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()
ax=fig.add_subplot(111,projection='3d')
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:


[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

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