We wish to use a GA to maximize the function, f(X) = 6X1X2X3 / (X1 +2 X2 +2 X3) , which is restricted by the relation that X1X2X3 = 16.

a. How would you encode this problem and why?

b. Show how you would handle the constraint using a penalty approach.

c. Using your encoding scheme, show a randomly generated population size of 6. Assume they each have the Fitness values shown.

Member-Fitness

1-963

2-1147

3-291

4-553

5-753

6 -1394

d. Given the random numbers as follows, r=(.1 .6 .7 .3 .2 .5 .8 .2 .4 .9 .1 .1 .4 .6 .8 .3 .6), use two body tournament selection to populate a mating pool. Explain how the random numbers are being used in your scheme. Illustrate the tournaments and the outcomes.

e. Illustrate crossover for your encoding and your mating pool using two appropriate members.

f. Show how mutation might occur with your encoding and a member of your population.