2. [20 points][MID] The graph k-coloring problem is stated as follows: Given an undirected graph G= (V, E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color e(r) such that 1< e(r)
2. [20 points][MID] The graph k-coloring problem is stated as follows: Given an undirected graph G= (V, E) with N vertices and M edges and an integer k. Assign to each vertex v in V a color e(r) such that 1< e(r)
Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
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![2. [20 points][MID] The graph k-coloring problem is stated as follows: Given an
undirected graph G = (V, E) with N vertices and M edges and an integer k. Assign to
each vertex v in V a color e(r) such that 1 < e{u) < k and c(u) # c(v) for every edge
(u, v) in E. In other words you want to color each vertex with one of the k colors you
have and no two adjacent vertices can have the same color.
For example, the following graph can be 3-colored using the following color assignments:
a=1,b=2,c=1,d%32,e=3,f=2.g33
a---b---c---g
d
Formulate the graph k-coloring problem as an evolutionary optimization. You may
use a vector of integer representation, OR any representation that you think is more
appropriate. you should specify:
• A representation.
• itness function. Give 3 examples of individuals and their fitness values if you
are solving the above example.
A set of mutation and/or crossover and/or repair operators. Intelligent operators
that are suitable for this particular domain will earn more credit.
• A termination eriterion for the evolutionary optimization which insures that you
terminate with a valid solution to the graph k-coloring problem if possible
without running indefinitely.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1288843a-a047-44bd-a093-fe09a3053548%2F85e08cc2-97bf-42e2-a5f4-04b2227da587%2F56mzx3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. [20 points][MID] The graph k-coloring problem is stated as follows: Given an
undirected graph G = (V, E) with N vertices and M edges and an integer k. Assign to
each vertex v in V a color e(r) such that 1 < e{u) < k and c(u) # c(v) for every edge
(u, v) in E. In other words you want to color each vertex with one of the k colors you
have and no two adjacent vertices can have the same color.
For example, the following graph can be 3-colored using the following color assignments:
a=1,b=2,c=1,d%32,e=3,f=2.g33
a---b---c---g
d
Formulate the graph k-coloring problem as an evolutionary optimization. You may
use a vector of integer representation, OR any representation that you think is more
appropriate. you should specify:
• A representation.
• itness function. Give 3 examples of individuals and their fitness values if you
are solving the above example.
A set of mutation and/or crossover and/or repair operators. Intelligent operators
that are suitable for this particular domain will earn more credit.
• A termination eriterion for the evolutionary optimization which insures that you
terminate with a valid solution to the graph k-coloring problem if possible
without running indefinitely.
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