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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. 3