Mathematical Definition
Input Domain
It is defined in the domain (-2π < Xi < 2π) where i = 1,2, ..., n. This function is not
smooth, and its derivatives are not well defined at the optimum (0, 0, ..., 0).
Global Minima
The Xin- She Yang N.2 Function has the global minimum f* = 0 at x* = (0, 0, ..., 0).
Description and Features
The Xin-She Yang N.2 Function is a multimodal function which is defined on n-dimensional spaces.
Non-differentiable
Non-linear
Non-Convex
Multimodal
Non-separable
Python Implementation
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% Author: Vanshita Tripathi
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
from numpy import*
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
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')
fig= plt.figure()
ax= plt.axes(projection='3d')
def f(x1,x2):
b= -(sin(x1*x1)+sin(x2*x2))
a= (abs(x1) +abs(x2))*exp(b)
return a
x1= linspace(2,-2)
x2= linspace(2,-2)
X1,X2= meshgrid(x1,x2)
ax.plot_surface(X1,X2,f(X1,X2), cmap='jet')
#ax.plot_wireframe(X1,X2,f(X1,X2), color='gray')
ax.set_xlabel('x1')
ax.set_ylabel('x2')
ax.set_zlabel('f(x1,x2)')
ax.view_init(10,10)
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.
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