DIXON-PRICE FUNCTION

Mathematical Definition

Input Domain

The function is usually evaluated on the hypercube xi ∈ [-10, 10], for all i = 1, …, d.

Global Minima

The function has global minimum

Description and Features

Python Implementation

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 from matplotlib import pyplot as plt
 from mpl_toolkits import mplot3d
 import numpy as np
 import matplotlib.pyplot as plt
 from matplotlib import cm
 def f(x1, x2): return ((x1-1)**2) + (2*(2*x2**2-x1)**2)
 x1 = np.linspace(-1, 10)
 x2 = np.linspace(-10, 10)
 X1, X2 = np.meshgrid(x1, x2)
 F = f(x1,x2)
 plt.contour(X1, X2, f(X1,X2))
 def plotter(E,A):
  fig = plt.figure(figsize=[12,8])
  ax = plt.axes(projection='3d')
  ax.plot_surface(X1, X2, f(X1, X2), cmap='autumn', alpha=0.3)
  ax.plot_wireframe(X1,X2,f(X1,X2),rcount=15,ccount=15)
  ax.view_init(elev=E, azim=A)
  ax.set_xlabel('X')
  ax.set_ylabel('Y')
  ax.set_zlabel('f(X, Y)')
  ax.contourf(x1, x2, f(X1, X2))
 print("solution 2")
 plotter(45,45)
 from ipywidgets import interactive
 iplot = interactive(plotter, E = (-90 , 90 ,5),
  A = (-90 , 90 ,5))
 iplot
 

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