EXERCISES FOR CHAPTER FOUR:
REPRESENTATION, RECOMBINATION
AND MUTATION
1. A genetic algorithm has individuals coded as binary strings of length 27. Mutation is applied
with a bit-wise probability of 1/27. What is the probability that the gene 17 is changed by
mutation?
 1/27

26/27
 1/17
 It is not possible to say without knowing what happens to the other genes
2. A number of on/off switches control a nuclear power plant, and a given configuration can be
thought of as a state. It is desired to search the space of possible states to find one that
minimises temperature fluctuations within the plant. It is decided to do this with a Genetic
algorithm.
What representation do you think would be most suitable for this problem if there are n
switches?

A string of n binary values.
 A vector of n floating point numbers.
 A string of values each coming from the set {1,…,n}
 A tree with n terminal nodes (leaves).
3. For which of the following types of problem representation would it not be suitable to use 2point crossover?
 A permutation representing the order in which a series of operations are performed in an
operating theatre.
 A binary string.

A sequence of integers representing moves from the set {left, right, ahead}.
 A vector of floating-point numbers representing angles within a design problem.
4. Which of the following offspring can not be created by one point crossover from two parents
000000 and 111111 ?
 111111.
 000000
 111000

110011
 011110
 001111
5. A mountain bike designer is trying to create a frame with certain desirable characteristics
under simulation. To do this they must specify a set of n tube lengths and m angles between
them. What representation do you think would be most suitable for this problem?
 A string of (n+m) binary values.
 A string of n values each between 1 and m.
 A vector of (n+m) floating point numbers.
 A permutation of the numbers 1 through to (n+m)

A tree with (n+m) terminal nodes (leaves).
6. It is necessary to schedule a set of appointments with a doctor so as to minimise the average
waiting time per patient. There are n patients. What representation do you think would be
most suitable for this problem?
 A string of n binary values.
 A vector of n floating point numbers.
 A string of values, each coming from the set 1 to n.
 A permutation of the numbers 1 to n.
 A tree with n terminal nodes (leaves).