Description
• Learning objectives.
At the completion of this project, you should be able to:
o Implement a method to generate all permutations of a set of numbers.
o Trace a Hamiltonian path through an undirected graph.
o Use brute force to find the minimum cost solution to a Traveling Salesperson
Problem.
• Background
o A Traveling Salesperson Problem (TSP) is an NP-complete problem. A salesman
is given a list of cities and a cost to travel between each pair of cities (or a list of
city locations). The salesman must select a starting city and visit each city exactly
one time and return to the starting city. His problem is to find the route (also
known as a Hamiltonian Cycle) that will have the lowest cost. (See
https://www.tsp.gatech.edu for more info)
• Problem
o You will be expected to use brute force to calculate the minimum cost paths for a
series of problems.
o Data for each problem will be supplied in a .tsp file (a plain text file).
• Hints
o Be careful of exponential explosion. 10 cities will have over 3 million possible
paths.
o The largest data set will be 12 cities.
o I strongly urge you to create reusable code. It will be needed for the future
projects.
o In the future projects, we will be dealing with MUCH larger datasets. So large
that brute force approach would not be possible.
• Deliverables
o Project report (2-3 pages). Describe how you generated the permutations
representing the tours. Show the route and the cost of the optimal tour for each
provided dataset.
o Well-commented source code for your project (You can use any language you
like, but I reserve the right to ask you to demo performance of your algorithm on
a new dataset).
o You don’t have to include a GUI with visual representation of the solutions for
this project, but it might be useful for your future TSP related projects in this
course.
Data Format: You can read about standard TSP problem files here:
https://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95
Data files for development and testing of your code will be generated using Concorde:
https://www.tsp.gatech.edu/concorde/index.html
Sample data file with 7 cities:
NAME: concorde7
TYPE: TSP
COMMENT: Generated by CCutil_writetsplib
COMMENT: Write called for by Concorde GUI
DIMENSION: 7
EDGE_WEIGHT_TYPE: EUC_2D
NODE_COORD_SECTION
1 87.951292 2.658162
2 33.466597 66.682943
3 91.778314 53.807184
4 20.526749 47.633290
5 9.006012 81.185339
6 20.032350 2.761925
7 77.181310 31.922361
Distance Formula: