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Branch and bound. branch and bound methods economize the search for the best trees by backing out of dead alleys. The Traveling Salesman Problem. the technique can be used to solve the traveling salesman problem. The Traveling Salesman Problem. an arbitrary route. d=5.4342.

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slide1

Branch and bound

branch and bound methods economize the search for the best trees by backing out of dead alleys.

slide2

The Traveling Salesman Problem

the technique can be used to solve the traveling salesman problem.

slide3

The Traveling Salesman Problem

an arbitrary route.

d=5.4342

slide4

The Traveling Salesman Problem

greedy, starting from each point

d=5.4342

d=2.8027

slide5

The Traveling Salesman Problem

solution found by branch and bound

d=5.4342

d=2.8027

d=2.7812

slide6

The Traveling Salesman Problem

the problem as a decision tree with 3 628 800 (10!) paths

1,2,3,4,5,6,7,9,8,10

1,2,3,4,5,6,7,9,10,8

1,2,3,4,5,6,7,10,8,9

1,2,3,4,5,6,7,10,9,8

1,2,3,4,5,6,7,8,9,10

1,2,3,4,5,6,7,8,10,9

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Branching and bounding

B&B walk along the paths, and keep track of the distance travelled and the shortest route as yet

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Branching and bounding

and bound back out of lengthypaths

distance=x

distance>x

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Branch and bound for parsimony

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Branch and bound for parsimony

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Branch and bound for parsimony

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Branch and bound for parsimony

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