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).

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The on-line accompaniment to the book Introduction to Evolutionary Computing