Exact solution of large-scale, asymmetric traveling salesman problems

A lowest-first, branch-and-bound algorithm for the Asymmetric Traveling Salesman Problem is presented. The method is based on the Assignment Problem relaxation and on a subtour elimination branching scheme. The effectiveness of the algorithm derives from reduction procedures and parametric solution of the relaxed problems associated with the nodes of the branch-decision tree. Large-size, uniformly, randomly generated instances of complete digraphs with up to 2000 vertices are solved on a DECstation 5000/240 computer in less than 3 minutes of CPU time. In addition, we solved on a PC 486/33 no-wait flow shop problems with up to 1000 jobs in less than 11 minutes and real-world stacker crane problems with up to 443 movements in less than 6 seconds.