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Branch & Bound

0. 7. 2. 3. 8. 6. 10. 4. 3. 8. 7. 12. 10. 9. 10. Branch & Bound. UPPER =  LOWER = 0. 0. 0. 7. 2. 3. 8. 6. 10. 4. 3. 8. 7. 12. 10. 9. 10. Branch & Bound. UPPER =  LOWER = 2. 0. 2. 0. 7. 2. 3. 8. 6. 10. 4. 3. 8. 7. 12. 10. 9. 10.

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Branch & Bound

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  1. 0 7 2 3 8 6 10 4 3 8 7 12 10 9 10 Branch & Bound UPPER =  LOWER = 0 0

  2. 0 7 2 3 8 6 10 4 3 8 7 12 10 9 10 Branch & Bound UPPER =  LOWER = 2 0 2

  3. 0 7 2 3 8 6 10 4 3 8 7 12 10 9 10 Branch & Bound UPPER =  LOWER = 3 0 2 3

  4. 0 7 2 3 8 6 10 4 3 8 7 12 10 9 10 Branch & Bound UPPER = 4 LOWER = 4 0 2 3 4

  5. 0 7 2 3 8 6 10 4 3 8 7 12 10 9 10 Branch & Bound UPPER = 3 LOWER = 3 0 2 3 4 3

  6. 0 7 2 3 8 6 10 4 3 8 7 12 10 9 10 Branch & Bound UPPER = 3 LOWER = 6 0 2 3 6 4 3

  7. 0 0 7 2 7 2 3 8 6 10 3 6 4 3 8 7 12 10 9 10 4 3 Branch & Bound UPPER = 3 LOWER = 7

  8. Branch & Bound Illustrated on Traveling Salesman Problem • Tasks are created dynamically • Upper bound is shared • Lower bound is local • Halve set of feasible tours: Explore only those paths that visit city 1 before city 2.

  9. 1 TSP instance Search Tree 0 1 1 1 4 4 0:0 3 2 1 1 4 1 02:4 01:1 03:1 1 4 4 1 012:2 013:5 031:5 032:2 Halve the set of feasible tours: Only visit tours where city 1 occurs before city 2. 1 032:2 0123:3 Partial tour 0, 3, 2 with cost lower bound = 2 1 01230:4 LEGEND

  10. 1 TSP instance Search Tree 0 1 1 1 4 4 0:0 3 2 1 1 4 1 02:4 01:1 03:1 1 4 4 1 012:2 013:5 031:5 032:2 upper bound = 1 032:2 0123:3 Partial tour 0, 3, 2 with cost lower bound = 2 1 01230:4 LEGEND

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