Branch-and-Bound Algorithm for Symmetric Travelling Salesman Problem

In this paper a branch-and-bound algorithm for the Symmetric Travelling Salesman Problem (STSP) is presented. The algorithm is based on the 1-tree Lagrangian relaxation. A new branching strategy is suggested in which the algorithm branches on the 1-tree edge belonging to the vertex with maximum degree in the 1-tree and having the maximum tolerance. This strategy is compared with branching on the shortest edge and the so-called strong branching, which is the branching on the edge with maximum tolerance also applied by Held and Karp (1971). The computational experiments show that proposed branching strategy provides better results on TSPlib benchmark instances.