Evolutionary Computation

Due: Tuesday, 24 September 2019 at the beginning of class

• Follow the general homework directions.
• Make sure you cite all your references and contacts.
• Chapters 4 and 5 in textbook.
• Problems
1. How big is the phenotype space for the eight-queens problem?
2. Design an incremental evolutionary algorithm for the eight-queens problem. That is, a solution must represent a way to place the queens on the chess board one by one. How big is the search space in your design?
3. Find a problem where EAs would certainly perform very poorly compared to alternative approaches. Explain why you expect this to be the case.
4. 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?
5. 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).
6. 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.
7. 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