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.