An Exact Two-Matching Based Branch and Bound Algorithm for the Symmetric Traveling Salesman Problem

Abstract : An algorithm is described for the symmetric traveling salesman problem (TSP) based on a bipartite two-matching lower bounding technique. The lower bound is strengthened by using the bipartite two-matching as the basis for a heuristic algorithm for the dual of integer two-matching. We use this dual as a lower bound for the symmetric traveling salesman problem in a branch and bound algorithm. Results are presented for random symmetric TSPs with up to 3000 cities. On Euclidean problems the two-matching bound is weaker than on random problems and algorithm performance deteriorates as a result. The algorithm successfully solves 11 of 15 Euclidean problems from the literature with sizes ranging from 17 to 99 cities.