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EASOM FUNCTION

Updated: Jul 18, 2021

Mathematical Definition

Input Domain

The function is usually evaluated on xi ∈ [-100, 100], for all i = 1, 2.

Global Minima

The function has one global minimum f (x*) = =-1 at x*=(π, π)

Description and Features

• The function is continuous.

• The function is non scalable.

• The function is defined on 2-dimensional space.

• The function is unimodal.

• The function is differentiable.

• The function is non-separable.

• The Easom function has several local minima and the global minimum has a small area relative to the search space.

Python Implementation

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from mpl_toolkits import mplot3d
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import sympy as sy
import math
from matplotlib import cm
#def f(x1, x2): return -((np.cos(x1)*np.cos(x2))*np.exp(-(x1-math.pi)**2-(x2-math.pi)**2)
def f(x1, x2): return -(np.cos(x1)*np.cos(x2))*np.exp(-(x1-math.pi)**2-(x2-math.pi)**2)
x1 = np.linspace(-100,100)
x2 = np.linspace(-100,100)
X1, X2 = np.meshgrid(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='rainbow', 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)')
print("solution 5")
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.