Egg holder has a deceptive landscape and is extremely hard function to optimize. This is
because it is characterized by an uneven plane having several dozen local minimums that easily
misleads the search agents.
Mathematical Definition
Input Domain
The function is usually evaluated on the square xi ∈ [-512, 512], for all i = 1, 2.
Global Minima
f(x0) = -959.6407 , at x0 = (512,404.2319)
Characteristics
The function is continuous.
The function is non- convex.
The function is defined on 2-dimensional space.
The function is multimodal.
The function is differentiable.
The function is non-separable.
The function is non-random.
The function is non-parametric.
Python Implementation
% Please forward any comments or bug reports in chat
Copyright 2021. INDUSMIC PRIVATE LIMITED.THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY FOR THE USE OF THIS PROGRAM. If software is modified to produce derivative works, such modified software should be clearly marked. Additionally, user can redistribute it and/or modify it under the terms of the GNU General Public License. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY. See the GNU General Public License for more details.
% for any support connect with us on help.indusmic@gmail.com
% Author: Parakh Jain
import matplotlib.pyplot as plt
from mpl_toolkits import mplot3d
from numpy import*
def f(x1,x2):
a=sqrt(fabs(x2+x1/2+47))
b=sqrt(fabs(x1-(x2+47)))
c=-(x2+47)*sin(a)-x1*sin(b)
return c
x1=linspace(-512,512,100)
x2=linspace(-512,512,100)
X1,X2=meshgrid(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),color='red',alpha=0.7)
ax.plot_wireframe(X1,X2,f(X1,X2),ccount=2,rcount=2, color='orange',alpha=0.8)
ax.view_init(elev=E,azim=A)
ax.set_xlabel('x1')
ax.set_ylabel('x2')
ax.set_zlabel('f(x1,x2)')
plt.show()
from ipywidgets import interactive
iplot=interactive(plotter,E=(-90,90,5),A=(-90,90,5))
iplotReferences:
[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.