Rose-Hulman Institute of Technology
Department of Mechanical Engineering
ME 536
Homework 3:
Course Value: 100 points
Computational Intelligence in Control Engineering
Deadline: April 21, 2016
a) (25 points) GA optimiziation of an integer function: Write a matlab program to demonstrate
convergence of the example shown in figure 15.4 of King. This exercise is intended to get you started with
GA programming.
b) (75 points) Write a matlab program to demonstrate use of the simple GA in solving the following
problem from homework set 1. Use ten (10) bit encoding for the free parameters (x1 , x 2 , x 3 ) Consider
the search space to be 0≤ x1 ≤1, 0≤ x 2 <1, 0≤ x 3 ≤1. Time permitting, you should experiment with the
population size, mutation rate, and number of generations allowed.
Unconstrained optimization from An Engineer's Guide to Matlab, Magrab et al. Prentice Hall, 2005.
Three carts, interconnected by springs and initially at an unstressed equilibrium state, are subjected to the
loads P1, P2, and P3 as shown below. The displacements of the carts from their original equilibrium
position (xi = 0: for all i) are sought by minimizing the potential energy of the system (PE):
PE 
1
T
T
X KX  X P
2
where
  k1  k 3  k 4
K  
k 3
 
k 4
k 3
k 2  k3  k 5
k 5
P  P1
X  x1
The input data are
k1 = 4500 N/m
k2 = 1650 N/m
k3 = 1100 N/m
k4 = 2250 N/m
k5 = 550 N/m
k6 = 9300 N/m
P2
x2
P3 
 k4


k 5
k4  k 5  k6  
T
x3 
T
P1 = 1100 N
P2 = 1800 N
P3 = 3300 N
Find the equilibrium position of the carts. [Answer: [ x1 , x2 , x3 ] = [ 0.348 0.723 0.370 ] ]
x2
x1
x3
P1
k4
k6
k2
P2
k1
k3
1
P3
k5
2
Figure 13.22 Spring-mass system of part b.
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