Mathematical Definition
Input Domain
It is defined in the domain (-1≤ xi≤1) for i= 1,2, …….. ,n, given that it is continuous in the range.
Global Minima
The Exponential function has one global minima f(x1*) = at x* = 0.
Description and Features
Unimodel Function.
Convex
Continuous
Differentiability
Non- Seperable
Python Implementation
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% Author: Vanshita Tripathi
import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits import mplot3d
import numpy as np
from numpy import*
from mpl_toolkits.mplot3d import Axes3D
%matplotlib notebook
plt.rcParams['figure.figsize'] = (6,4)
plt.rcParams['figure.dpi']=150
fig=plt.figure()
ax=fig.add_subplot(111,projection='3d')
ax= plt.axes(projection='3d')
def f(x1,x2):
a= -exp(-0.5*(x1*x1 + x2*x2))
return a
x1= linspace(-1,1)
x2= linspace(-1,1)
X1,X2= meshgrid(x1,x2)
ax.plot_surface(X1,X2,f(X1,X2), cmap='jet')
ax.set_xlabel('x1')
ax.set_ylabel('x2')
ax.set_zlabel('f(x1,y1)')
ax.view_init(100,100)
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.
[2] Hongmei Ma, Cheng Peng, Jinying Gan, Yonghong den, “An Optimization Algorithm for Exponential Curve Model of Single Pile Bearing Capacity”, https://doi.org/10.1007/s10706-020-01663-1(0123456789().,-volV)( 01234567.
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