The Travelling Salesman Problem

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The Travelling Salesman Problem

  1. 1. The Travelling Salesman Problem By Matt Leonard & Nathan Rodger
  2. 2. So What Is The Problem? <ul><li>The problem is: when given an amount of cities, and the costs of travelling from one city to the next, what is the least costly trip you could make to visit each city once before returning to your start city. (This is the only city you can visit twice) </li></ul><ul><li>So, For Example… </li></ul>
  3. 3. Is there a route that takes you through every city and back to the start point ‘A’ for less than 520? The answer is yes. The solution is ABCGFDEA A G B F C E D 100 80 70 70 120 60 40 70 90 110 50 30
  4. 4. So can a computer solve this problem? <ul><li>Well in theory yes it can, however there are some problems… </li></ul><ul><li>An exact solution was found for 15,112 German towns in 2001. </li></ul><ul><li>If a computer was asked to calculate the solution it would take…. </li></ul>22.6 years!
  5. 5. <ul><li>In 2005, the travelling salesman problem was tested visiting all 33,810 points in a circuit board. </li></ul><ul><li>It was solved using Concorde </li></ul><ul><li>A tour of length 66,048,945 units was found and it was proven that no shorter tour exists. </li></ul><ul><li>The computation took approximately 15.7 CPU years. </li></ul><ul><li>(Concorde is a program used for solving the TSP) </li></ul>
  6. 6. <ul><li>So if you thought computers could do things quickly… check this out. </li></ul><ul><li>In 2006 an instance with 85,900 points was tested. </li></ul><ul><li>Once again it was solved using Concorde. </li></ul>This would take a WHOPPING 136 computer years!!!
  7. 7. So what does this all mean? <ul><li>Computers can work out the TSP, but increase the amount of units involved and the computer starts to struggle. </li></ul><ul><li>Devising algorithms for finding exact solutions will only work reasonably fast for relatively small problem sizes. </li></ul><ul><li>So when you increase the set of instructions, a computer will take longer to process the data. </li></ul>
  8. 8. <ul><li>We hope you understand more about the travelling salesman problem. </li></ul><ul><li>We thank you for viewing this presentation and hope you have learnt a little bit more about computers in general. </li></ul><ul><li>Any Questions..? </li></ul>

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