HW #3
–
Evolutionary Computation
1.
Explain the effect of selection, crossover and mutation in evolutionary computation. How is
the population affected by the use of each one of these operators? What happens if you use a
relatively high rate of mutation?
Wha
t is a possible problem that might occur in an algorithm
that uses elitism?
2.
Let the fitness f of bit string x with length
L
=4 to be the integer represented by the binary
number x (e.g. f(0011) = 3, f(1111) = 15). Assume that the current population is:
10
10
1000
0100
0110
1100
a.
Is it possible for a GA to generate an individual with the maximum fitness without using
mutation, but only single point crossover? If so, give an example.
b.
If mutation has a rate other than 0, could the GA possibly generate t
he fittest individual?
Give an example.
3.
Consider the following
fitness function
:
f
(<bitstring>) = number of 1’s in the bitstring where
both
adjacent bits are 0’s
For example, f(010110100) = 2, f(100011011) = 0, and f(010101010
) = 4.
(Notice that 1's
in the first or last position in the string are not counted in the fitness function,
even if adjacent to a 0.)
Assume the design of our genetic algorithm is:
(a)
Create an initial population containing 4 random 9

bit strings.
(b)
Discard the 2 least

fit ones (bre
ak ties randomly).
(c)
Do a
cross

over
using the 2 most fit. The 2 children that result and their parents
constitute the next generation.
(d)
Randomly
mutate
1 bit in 1 string in the population.
(e)
Go to step (b)
Start with the initial population below and show what
the
next
two generations
might look
like. Briefly explain your reasoning.
Initial Population
011110110
011001011
101101110
000010101
4.
In a Genetic Algorithm, suppose that two potential parents are given by
Assuming the numbering goes from left to right and that
1
=
4
and
2
=
8
, show th
e result of
two

point crossover.
5.
Suppose a 3

gene chromosome is represented by floating point numbers, and 2 parents are
shown below.
8.5
2.4
3.9
7.1
1.5
6.2
Using a 2
parent
–
2 offspring model, show the resulting offspring produced by arithmetic
cross

over, assuming
1
= 0.8 and
2
= 0.2.
6.
Consider
a
function maximization application of a GA
. Suppose
the 5 chromosomes at a
given generation have fitness values
listed
below.
f(x
1
) = 55
f(x
2
) = 24
f(x
3
) = 8
f(x
4
) = 19
f(x
5
) = 42
Construct the “roulette wheel” for selection of parents for crossover.
7.
Consider the problem below and discuss how you would find a solution using evolutionary
computation. Discuss the repre
sentation of the chromosome, the fitness function, and
whether any special mutation and cross

over operators would be required. Justify your
approach.
You are given a list of 100 items, each with a weight and a utility value. The problem is
to select an o
ptimal set of items from the list, up to 6 items total, such that the weight is
less than 20 pounds, and the utility is maximized.
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
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