CS 411 Fall 2025  >  Outline for December 3, 2025

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CS 411 Fall 2025
Outline
for December 3, 2025

Outline

Branch-and-Bound [L 12.2]

• Description
  • Branch-and-Bound is a method of pruning the state-space tree for optimization problems.
  • We need a way to find, for each node in the state-space tree, a bound on the value of the objective function for every feasible solution that can be obtained from the partial solution that the node represents.
    • For a maximization problem, we need an upper bound. For a minimization problem, we need a lower bound.
  • Procedure. Traverse the state-space tree, keeping track of the best value of the objective function found so far. If the bound we obtain for a node is not as good as that best-so-far value, then do not visit that node’s children (“prune”).
• Best First version
  • A node whose bound is further in the desired direction (greater for a maximization problem, less for a minimization problem) is considered to be more promising than another node.
  • Idea. At each step, find the most promising node whose children have not been visited. Visit the children of this node next.
  • Hopefully, this lets us find better solutions early, resulting in more pruning and thus better performance.
  • This is called best-first branch-and-bound.
• Example
• Notes
  • Branch-and-bound has been found, in practice, to improve performance for many problems.
  • However, generally, branch-and-bound offers no guarantees of better performance.