Branch and Bound.

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Presentation transcript:

Branch and Bound

Branch-and-Bound An enhancement of backtracking Applicable to optimization problems For each node (partial solution) of a state-space tree, computes a bound on the value of the objective function for all descendants of the node (extensions of the partial solution) Uses the bound for: ruling out certain nodes as “nonpromising” to prune the tree – if a node’s bound is not better than the best solution seen so far guiding the search through state-space

Assignment Problem Select one element in each row of the cost matrix C so that: no two selected elements are in the same column the sum is minimized Lower bound: Any solution to this problem will have total cost at least: 2 + 3 + 1 + 4 (or 5 + 2 + 1 + 4)

Assignment Problem

Travelling Salesman Problem