Xin-She Yang N.2 Function

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.

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.

#optimization #benchmarkfunction