An Introduction to Genetic Algorithms - Boente

COMPUTER EXERCISES
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Chapter 2: Genetic Algorithms in Problem Solving
Implement a genetic programming algorithm and use it to solve the "6−multiplexer" problem (Koza
1992). In this problem there are six Boolean−valued terminals, {a0, a1, d0,d1, d2, d3}, and four
functions, {AND, OR, NOT, IF}. The first three functions are the usual logical operators, taking two,
two, and one argument respectively, and the IF function takes three arguments. (IF X Y Z) evaluates
its first argument X. If X is true, the second argument Y is evaluated; otherwise the third argument Z
is evaluated. The problem is to find a program that will return the value of the d terminal that is
addressed by the two a terminals. E.g., if a0 = 0 and a1 = 1, the address is 01 and the answer is the
value of d1. Likewise, if a0 = 1 and a1 = 1, the address is 11 and the answer is the value of d3.
Experiment with different initial conditions, crossover rates, and population sizes. (Start with a
population size of 300.) The fitness of a program should be the fraction of correct answers over all 2 6
possible fitness cases (i.e., values of the six terminals).
Perform the same experiment as in computer exercise 1, but add some "distractors" to the function
and terminal sets—extra functions and terminals not necessary for the solution. How does this affect
the performance of GP on this problem?
Perform the same experiment as in computer exercise 1, but for each fitness calculation use a random
sample of 10 of the 2 6 possible fitness cases rather than the entire set (use a new random sample for
each fitness calculation). How does this affect the performance of GP on this problem?
Implement a random search procedure to search for parse trees for the 6−multiplexer problem: at each
time step, generate a new random parse tree (with the maximum tree size fixed ahead of time) and
calculate its fitness. Compare the rate at which the best fitness found so far (plotted every 300 time
steps—equivalent to one GP generation in computer exercise 1) increases with that under GP.
Implement a random−mutation hill−climbing procedure to search for parse trees for the 6−multiplexer
problem (see thought exercise 2). Compare its performance with that of GP and the random search
method of computer exercise 4.
Modify the fitness function used in computer exercise 1 to reward programs for small size as well as
for correct performance. Test this new fitness function using your GP procedure. Can GP find correct
but smaller programs by this method?
Repeat the experiments of Crutchfield, Mitchell, Das, and Hraber on evolving r = 3 CAs to solve the
problem. (This will also require writing a program to simulate cellular automata.)
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