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Solving Traveling Salesman Problem: Algorithms Comparison

Compare Nearest Unvisited Neighbor, Sweep Algorithm, and Integer Programming for points A, B, C, D, E, and Z with different distances. Nearest Neighbor total distance: 17.06, Sweep Heuristic total distance: 15.43, Integer Programming with two solutions - 14.25 and 15.43.

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Solving Traveling Salesman Problem: Algorithms Comparison

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  1. HW06 Solve The Traveling Salesman Problem Using Three Algorithms.1. Nearest Unvisited Neighbor2. Sweep Algorithm3. Integer Programming

  2. Location Of Points

  3. Drawing C B 5 4 3 2 1 0 Z D E A 0 1 2 3 4 5

  4. Distances

  5. Nearest Neighbor Begin at A Go to E (3.16) From E Go to D (2.24) From D Go to C (2.83) From C Go to B (1.00) From B Go to Z (2.00) From Z return to A (5.83) Total Distance: 17.06

  6. Nearest Neighbor Drawing C B 5 4 3 2 1 0 Z D E A 0 1 2 3 4 5

  7. Sweep Heuristic Total Distance: 15.43

  8. Sweep Heuristic Drawing C B 5 4 3 2 1 0 Z D E A 0 1 2 3 4 5

  9. Integer Programming (1) • AMPL generated Subtours • A-D-E-A and B-C-Z-B • With the total distance of 14.25

  10. Integer Prog Drawing (1) C B 5 4 3 2 1 0 Z D E A 0 1 2 3 4 5

  11. Integer Programming (2) • Add in constraints to eliminate subtour • Total Distance is 15.43

  12. Integer Prog Drawing (2) C B 5 4 3 2 1 0 Z D E A 0 1 2 3 4 5

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