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 d= an arbitrary route.

The Traveling Salesman Problem d= d= greedy, starting from each point

The Traveling Salesman Problem d= d= d= solution found by branch and bound

The Traveling Salesman Problem start … ,2,3,4,5,6,7,8,9, ,2,3,4,5,6,7,8,10, ,2,3,4,5,6,7,9,8, ,2,3,4,5,6,7,9,10, ,2,3,4,5,6,7,10,8, ,2,3,4,5,6,7,10,9, the problem as a decision tree with (10!) paths

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 distance=x distance>x and bound back out of lengthy paths

Branch and bound for parsimony a b c a d b c a c b d a c b d a c b e a c d e c e b d a e b d c a d b e a d c e b a d b e c a d b c e d e b c a e a b c d a e c d b b e c d a a b c d e a b c e d a b d e c a d b c

Branch and bound for parsimony

Branch and bound for parsimony