Name _____________
CS472/572 Evolutionary Computation
First Exam
This is a closed note, closed book exam. The abbreviation GA is used for Genetic
Algorithm throughout.
1. (15 points) Consider a real valued optimization problem with 50 variables, all in the
range -512 to +512. Below are 3 mutation approaches. What are the weaknesses of each
approach?
a) Change all of the 50 values by either +1 or -1.
b) Change one value (selected randomly) by 0.1, if this doesn’t improve the fitness,
change the same value by -0.1. If that doesn’t improve fitness, repeat the process,
picking a different value to change each time the process is repeated.
c) With 50% probability change each of the values (i.e. on average half of the values
are changed), the new value for each changed variable is drawn randomly from
the full range of -512 to +512.
2. (33 points) Match each of the definitions to the appropriate term or terms from the
following list. Note that there are some extra terms.
_______ Type of evolutionary algorithm in which the whole population is
replaced in every iteration.
_______ Type of search algorithm in which the probability of keeping a new,
worse solution gets smaller as the algorithm proceeds.
_______ Crossover as shown below:
01011100
11100101
01100100
11011101
_______ Crossover as shown below:
01011100
11100101
01000101
11111100
_______ A selection operator based on the relative fitness ranking of the
individuals.
_______ A selection operator based on the relative fitness values of the
individuals.
_______ A solution that has no neighbors with a better fitness.
_______ Optimization technique with a “population of size 1” that only moves to
better solutions.
_______ Form of GA mutation in which a small change is made to many of the
values in the individual.
_______ Form of GA mutation used with permutation representations.
Terms:
a. uniform crossover
b. swap mutation
c. insert mutation
d. creep mutation
e. evolutionary strategies
f. GA
g. steady-state
h. 2-point crossover
i. Order crossover
j. tournament selection
k. roulette wheel selection
l.
m.
n.
o.
p.
q.
r.
s.
t.
meta-GA
generational
1-point crossover
local optima
global optima
fitness landscape
fixed bit
simulated annealing
hill climbing
3. (10 points) In the 0/1 knapsack problem you have N items, each item has a weight (wi)
and a value (vi). The goal is to find the subset of the N items that have the maximum
value and total weight less than some maximum (Wmax).
For example, if you have the following 9 items:
Item
1
2
3
4
5
6
7
8
Num:
Weight
5
7
3
2
8
11
3
1
Value
5
6
2
3
11
10
5
1
If you select items 2, 5, and 7 the total weight is 7+8+3 = 18 and the total value is
6+11+5 = 22.
Now, consider a 0/1 knapsack problem with N = 1,000, i.e. 1000 items. You would like
to solve it using a generational GA with elitism of two (two copies of the best individual
are made each generation) and a population size of 1,000 running for 1,000 generations.
What is an upper bound on the fraction of all possible solutions will the GA test? Be as
exact as possible and explain your answer.
4. (5 points) Draw the landscape of a problem that would be very difficult for hill
climbing, but reasonable for a GA.
5. (20 points) A clique is a set of completely interconnected points in a graph (see
below). The maximum clique problem is to find the largest clique in a graph. Imagine
designing a GA to solve the maximum clique problem for a graph with 100 nodes.
4
7
Sample graph, the maximum
1
clique is shown with dashed
8
lines (vertices: 1,4,5,7,8).
5
Another, non-maximum, clique
is shown with dotted lines
(vertices: 5, 8, 9).
2
9
6
3
How would you represent potential solutions? I.e. what would an individual/potential
solution look like? Why would you use that representation?
How would you measure fitness? Why?
How would you perform mutation? Why?
How would you perform crossover? Why?
6. (5 points) What are the two most important differences between a GA and simulated
annealing?
7. (4 points) Describe one practical problem with roulette wheel selection.
8. (8 points) The following is a list of changes that you could make to an evolutionary
algorithm. Circle all of the changes that are likely to make the population converge faster
(i.e. that are likely to make all of the individuals in the population become more similar
faster). Underline all of the changes that are likely to make the population converge
slower (i.e. that are likely to make all of the individuals in the population remain different
for longer). Some changes may not do either, leave those alone. You may explain your
answers.
a) Increasing the tournament size when using tournament selection.
b) Increasing the probability of mutating each value in an individual.
c) Increasing the number of elite individuals.
d) Switching from generational to steady-state