EGGHOLDER FUNCTION

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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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))
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