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ACKLEY N.2 FUNCTION

Updated: Jul 1, 2021




Mathematical Definition



Input Domain


The function can be defined on any input domain but it is usually evaluated on x ∈ [−32, 32] and y ∈ [−32, 32].


Global Minima


The global minimum of the function is at f(x∗ ) = −200 located at x ∗ = (0, 0).


Description and Features


The function is convex.

The function is defined on 2-dimensional space.

The function is non-separable.

The function is differentiable.



Python Implementation

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from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
import numpy as np

def f(x,y):
        return -200*np.exp(-0.2*np.sqrt(x**2 + y**2))
        
X = np.linspace(-32,32)
Y = np.linspace(-32,32)

x,y = np.meshgrid(X,Y)
F = f(x,y)

fig = plt.figure(figsize=(9,9))
ax = plt.axes(projection='3d')
ax.contour3D(x,y, F,450)

ax.set_title('Plot Ques 2')
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('F')
ax.view_init(21,45)
plt.show()


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

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