2. Explain how a valid genotype can be represented as a partial permutation of integers,
The clique problem is to find cliques in a graph.
A clique is a set of vertices that are all adjacent - connected - to each other.
A 4-clique is a set of 4 vertices that are all connected to each other.
So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force
(Image taken from the Wikipedia 'Clique Problem' page.)
You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it.
Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search.
For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a 4-clique.
To achieve this task you would need to:
- develop an understanding of the problem and the nature of the search space
- figure out how to represent solutions and calculate fitness
- figure out ways to perform techniques such as mutation, crossover and termination
...and so the questions below are designed to take you through some of those processes.
You are expected to fill in any gaps in your knowledge of combinatorial mathematics through independent study.
2. Explain how a valid genotype can be represented as a partial permutation of integers, providing an example for the case n=7.
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