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Branch and bound method
The branch-and-bound method is used to solve optimization problems by systematically enumerating all possible solutions through a state space tree. It improves on backtracking by computing bounds at each node to prune unpromising branches. For the traveling salesperson problem, it finds an initial feasible tour then uses a bounding heuristic based on minimum costs to prune branches that cannot lead to an optimal solution. It searches the tree in a best-first order until proving the initial tour is optimal without exploring the entire tree.
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Introduction to Branch-and-Bound method for solving optimization problems, focusing on the Traveling Salesperson Problem.
Explanation of B&B as a state space tree method, describing traversal types and the bounding heuristic for node evaluation.
Introduction to the Traveling Salesperson Problem, including distance representation and the greedy method for initial candidate tours.
Definition of bounding heuristic using actual cost and minimum completion costs to estimate tour costs in TSP.
Steps to prune non-promising nodes in TSP optimization, establishing a candidate tour of length 28 with confirmation of minimality.
Introduction to the Knapsack Problem, focusing on maximizing profit subject to weight constraints.
Explains how to use B&B for the 0/1 Knapsack Problem including solving techniques and deriving upper bounds.
Description of finding optimal solutions in Knapsack using the greedy method and best-first search strategies.
Terminology on the state of nodes in B&B for Knapsack, emphasizing termination criteria for suboptimal nodes.
Concluding the presentation with thanks.
