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
The function is continuous.
The function is scalable.
The function is unimodal.
The function is differentiable.
The function is non-separable.
The function is defined on d-dimensional space.
Python Implementation
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% Author: Ayushi Manish Shukla
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.