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Rotated Hyper-Ellipsoid Function

Updated: Mar 30, 2022

Mathematical Definition

Input Domain

It can be defined into any input domain but usually evaluated on the hypercube ๐‘ฅ๐‘– โˆˆ [โˆ’65.536,65.536], for all ๐‘– = 1, โ€ฆ . , ๐‘‘.

Global Minima

The function has one global minimum ๐‘“(๐‘ฅ โˆ— ) = 0, ๐‘Ž๐‘ก ๐‘ฅ โˆ— = (0, โ€ฆ ,0).

Description and Features

The function is continuous function.

The function is convex function.

The function is referred as sum squareโ€™s function.

It is also an extension of the axis parallel hyper- ellipsoid function.

The function is unimodal function.

Python Implementation

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import matplotlib.pyplot as plt
import numpy as np
from numpy import *
from numpy import cos
from numpy import pi
from numpy import abs,sqrt

from numpy import meshgrid
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm

def f(x1,x2):  
 return (2*(x1*x1)+(x2*x2))
x1= np.linspace(-65.536,65.536,500)
x2= np.linspace(-65.536,65.536,500)


axis.set_title('Rotated Hyper-Ellipsoid Function')
axis.contour3D(x1, x2, results,450)
axis.plot_surface(x1,x2,results, cmap=cm.YlGn)


[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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