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
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% 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.
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