TSP Branch-and-Bound Algorithm: Solving Optimal Tour Problems, Study notes of Algorithms and Programming

Download TSP Branch-and-Bound Algorithm: Solving Optimal Tour Problems and more Study notes Algorithms and Programming in PDF only on Docsity! COMP157 Fall 2007 TSP Branch-and-Bound Algorithm ALGORITHM tsp_branch_and_bound(graph) Inputs: graph, the graph Output: the best (cheapest) tour, possibly null best_tour  null // priority queue stores paths in ascending order of their lower bound on potential tour cost queue  new priority queue initial_path  path containing only node ‘a’ compute lower bound for initial_path queue.enqueue(initial_path) while queue is not empty do: // get the path with best estimated cost path_to_expand  queue.dequeue // If lower bound on best path_to_expand is worse than best tour, there's no point in continuing if best_tour is not null and path_to_expand.lower_bound >= best_tour.cost do: return best_tour // Is path_to_expand a nearly completed tour? if path_to_expand is complete except for a return to the start node do: // Can we complete the tour? if there is an edge in the graph to complete path_to_expand do: // complete this tour tour  copy of path_to_expand tour.add(edge back to start) // is this tour better than best we’ve seen so far? if best_tour is null or tour.cost < best_tour.cost do: best_tour  tour else do: // Generate all extensions from path_to_expand and put them in the queue. for node  'a' .. graph.lastNode do: if path_to_expand does not already visit node and graph has an edge from last node in path_to_expand to node do: // create extended path extended_path  copy of path_to_extend extended_path.add(node) compute lower bound for extended_path // only put extended path in queue if it is potentially better than best tour if best_tour is null or extended_path.lower_bound < best_tour.cost do: queue.enqueue(extended_path) return best_tour