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CS 325 Project 4: The Travelling Salesman Problem (TSP)
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In this project you will have fun trying out ideas to solve a very hard problem: The Traveling Salesman
Problem (TSP).
You are given a set of n cities and for each pair of cities c1 and c2, the distances between them d(c1, c2).
Your goal is to find an ordering (called a tour) of the cities so that the distance you travel is minimized.
The distance you travel is the sum of the distances from the first city in the ordering to the second city,
plus the distance second city to the third city, and so on until you reach the last city, and then adding the
distance from the last city to the first city. For example if the cities are Seattle, Portland, Corvallis and
Boise. The total distance traveled visiting the cities in this order is:
d(tour) = d(Seattle,Portland) + d(Portland, Corvallis) + d(Corvallis,Boise) + d(Boise, Seattle)
In this project, you will only need to consider the special case where the cities are locations in a 2D grid
(given by their x and y coordinates) and the distance between two cities c1 = (x1, y1) and c2 = (x2, y2) is
given by their Euclidean distance. To avoid floating point precision problems in computing the square-
root, we will always round the distance to the nearest integer. In other words you will compute the
distance between cities c1 and c2 as:
For example, if the three cities are given by the coordinates c1= (0, 0), c2 = (1, 3), c3 = (6, 0), then a tour
that visits the cities in order c1 –> c2 –> c3 – >c1 has the distance
d(tour) = d(c1, c2) + d(c2, c3) + d(c3, c1)
where
= 3
CS 325 Project 4: The Travelling Salesman Problem (TSP)
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= 6
= 6
So that d(tour ) = 3 + 6 + 6 = 15.
Project Specification
Your group will research at least three different algorithms for solving the TSP problem. There is much
literature on methods to “solve” TSP please cite any sources you use. You will design and implement at
least one algorithm for finding the best tour you can for the TSP problem. TSP is not a problem for
which you will be able to easily find optimal solutions. It is difficult. Your goal is to find the best solution
you can in a certain time frame. Use any programming language you want that runs on
flip2.engr.oregonstate.edu.
Your program must:
Accept problem instances on the command line
Name the output file as the input file’s name with .tour appended (for example input
tsp_example_1.txt will output tsp_example_1.txt.tour)
Compile/Execute correctly and without debugging on flip2.engr.oreognstate.edu according to
specifications and any documentation you provide.
Input specifications:
A problem instance will always be given to you as a text file.
Each line defines a city and each line has three numbers separated by white space.
o The first number is the city identifier
o The second number is the city’s x-coordinate
o The third number is the city’s y-coordinate.
Output specifications:
You must output your solution into another text file with n+1 lines, where n is the number of
cities.
CS 325 Project 4: The Travelling Salesman Problem (TSP)
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The first line is the length of the tour your program computes.
The next n lines should contain the city identifiers in the order they are visited by your tour.
o Each city must be listed exactly once in this list.
o This is the certificate for your solution and your solutions will be checked. If they are
not valid you will not receive credit for them.
Example instances: We have provided you with three example instances. They are available on Canvas
and are provided according to the input specifications.
tsp_example_[*].txt Input files
tsp_example_[*].txt.tour Example outputs corresponding to these three input cases.
The optimal tour lengths for example instances 1, 2, and 3 are 108159, 2579 and 1573084,
respectively. Clearly these do not match the values in the tour files. You should use these values to
evaluate your algorithm. For full credit it is required that the ratio of
(your solution)/(optimal solution) <= 1.25.
In an unlimited amount of time.
Testing
A testing procedure tsp-verifier.py is given that we will use to verify your solutions. Usage to test
example an instance is: (NOTE: requires TSPAllVisitied.py)
python tsp-verifier.py inputfilename solutionfilename
You should test that your outputs are correct. By “correct” we mean that the distances have been
computed correctly not that the solution is optimal.
Competition
We will hold a completion. The competition will require your program to find the best solution possible
to one or more test instances within a fixed amount of time (e.g. 3 minutes). The competition instances
will be available on Monday 3/13/17 at 8:00 am PST. You will not be told the optimal tour length for
these instances. You will post your results to the competition instances to the competition discussion
board.
Project Report
You will submit a project report containing the following:
A description of at least three different methods/algorithms for solving the Traveling Salesman
Problem. Summarize any research you did.
A verbal description of your algorithm(s) as completely as possible. You may select more than
one algorithm to implement.
A discussion on why you selected the algorithm(s).
Pseudo code
CS 325 Project 4: The Travelling Salesman Problem (TSP)
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Your “best” tours for the three example instances and the time it took to obtain these tours. No
time limit.
Your best solutions for the competition test instances. Time limit 3 minutes and unlimited time.
Submission
All files (including a REDME), solutions and report must be zipped and submitted to TEACH by
Friday 3/17/17 at 11:59pm PST. Only the report will be submitted to Canvas.
Check List
Does your program correctly compute tour lengths for simple cases?
Does your program read input files and options from the command line?
Does your program meet the output specifications?
Did you check that you produce solutions that verify correctly?
Did you find solutions to the example instances?
Did you find solutions to the competition instances? Post your results to the competition
discussion board to be eligible for extra-credit points.
Does your code compile/run without issue according to your documentation?
Have you submitted your report to Canvas? In the comment section post the onid username of
the person who submitted to TEACH.
Have you submitted your report, your solutions to the test cases, your source code and README
file to TEACH?
