We report the solution to optimality of ten large-scale symmetric travelling salesman problems. The travelling salesman problem (TSP) is one of the standard problems of the Operations ...

This paper elaborates a method of attack on traveling-salesman problems, proposed by the authors in an earlier paper, in which linear programming is used to reduce the combinatorial magnitude of such ...

Is it hopeless to try to compute the shortest route to visit a large number of cities? Not just a good route but the guaranteed shortest. The task is the long-standing challenge known as the traveling ...