Implementing Domino-Parity Inequalities for the Traveling Salesman Problem

We describe an implementation of Letchford’s domino-parity inequalities for the (symmetric) traveling salesman problem. The implementation includes pruning methods to restrict the search for dominoes, a parallelization of the main domino-building step, heuristics to obtain planar-support graphs, a set of safe-shrinking routines, a random-walk heuristic to extract additional violated constraints, and a tightening routine to allows us to modify existing domino-parity inequalities as the LP solution changes. We report computational results showing that combining the new separation algorithms with the Concorde TSP code allow us to substantially raise the linear programming bounds that are obtained.