Branch and bound

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# Branch and bound - PowerPoint PPT Presentation

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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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

The Traveling Salesman Problem

greedy, starting from each point

d=5.4342

d=2.8027

The Traveling Salesman Problem

solution found by branch and bound

d=5.4342

d=2.8027

d=2.7812

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

Branching and bounding

and bound back out of lengthypaths

distance=x

distance>x

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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