Full Sail University Graph Theory and Optimization Optimization Project Objective • Explore Applications of Graph Theory and Combinatorics • Identify why c

Full Sail University Graph Theory and Optimization Optimization Project
Objective
• Explore Applications of Graph Theory and Combinatorics
• Identify why certain problems are difficult to solve efficiently
• Explore the use of Heuristics
Instructions
Answer all numbered questions in the Document
Introduction
The traveling salesman problem is stated as “Given a list of cities and the distances between each pair of cities, what is the
shortest possible route that visits each city and returns to the origin city?”
Brute Force Search
1. Write all possible circuits for the graph in the form
Example:
There will be 24 possible circuits to list
2. For each circuit, calculate the total distance traveled
The total distance is the sum of each distance on the route
3. Identify the Optimal Circuit
The optimal path is the one with the shortest distance
Reflection
4. What about the Brute Force Search process of finding the optimal circuit using the above technique requires so
many steps?
What would the process be like for finding the optimal path for larger graphs (10, 20, 100 nodes)
5. Describe the method you could would use to find a good solution instead of a Brute Force Search?
A heuristic is a technique for finding an approximate solution based on discovery when finding a optimal one is too difficult
Optimization Project
Heuristic Challenge
Doing a brute force search (trying every path) is prohibitively difficult for finding a solution for a 7 point graph. Come up with an
approach that will allow you to find a good low cost circuit (if not necessarily the best)
6. Select a “good” circuit in the the following graph and give the cost of traversing it
The lowest cost circuit in the class gets 15 points
Any score in the to 20% of circuit will get 12 points
Any score in the top 50% of circuit will get 10 points
Any valid circuit will earn 5 points
This is weighted adjacency matrix for the graph
you are looking to traverse. For simplicity sake
the graph is non-directed
You can use this information to draw a graph is you want to
visualize the graph. See question 9 in project 2 for a refresher. TRAVELING SALESMAN PROBLEM
Discrete Math
Graph Theory and Optimization
Optimization Project
Objective
•
Explore Applications of Graph Theory and Combinatorics
Identify why certain problems are difficult to solve efficiently
•
Explore the use of Heuristics
•
Instructions
Answer all numbered questions in the Document
Introduction
The traveling salesman problem is stated as “Given a list of cities and the distances between each pair of cities, what is the
shortest possible route that visits each city and returns to the origin city?”
Brute Force Search
1. Write all possible circuits for the graph in the form
Example:
There will be 24 possible circuits to list
2. For each circuit, calculate the total distance traveled
The total distance is the sum of each distance on the route
3. Identify the Optimal Circuit
The optimal path is the one with the shortest distance
Reflection
4. What about the Brute Force Search process of finding the optimal circuit using the above technique requires so
many steps?
What would the process be like for finding the optimal path for larger graphs (10, 20, 100 nodes)
5. Describe the method you could would use to find a good solution instead of a Brute Force Search?
A heuristic is a technique for finding an approximate solution based on discovery when finding a optimal one is too difficult
Optimization Project
Heuristic Challenge
Doing a brute force search (trying every path) is prohibitively difficult for finding a solution for a 7 point graph. Come up with an
approach that will allow you to find a good low cost circuit (if not necessarily the best)
6. Select a “good” circuit in the the following graph and give the cost of traversing it
The lowest cost circuit in the class gets 15 points
A
B
C
D
E
F
G
A
0
12
32
24
9
21
17
B
12
0
10
14
30
2
20
C
32
10
0
5
12
10
16
D
24
14
5
0
22
31
4
E
9
30
12
22
0
12
24
F
21
2
10
31
12
0
7
G
17
20
16
4
24
7
0
Any score in the to 20% of circuit will get 12 points
Any score in the top 50% of circuit will get 10 points
Any valid circuit will earn 5 points
This is weighted adjacency matrix for the graph
you are looking to traverse. For simplicity sake
the graph is non-directed
You can use this information to draw a graph is you want to
visualize the graph. See question 9 in project 2 for a refresher.
Optimization Project
Rubric
Excellent
Good
Fair
Missing
Questions
15 Points
Completely answered
question or best
possible answer
10 Points
Answer is relevant
but not the best
possible
5 Points
Answer incomplete
or off topic
0 Points
Answer missing
Submission
10 Points
Follows submission
instructions
5 Points
Did not follow
naming convention
2 Points
Project not gradable
0Points
Not turned in on
time

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