# 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 2-point 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).