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 ...

The task is the long-standing challenge known as the traveling salesman problem, or TSP for short. Finding a method that can quickly solve every example of the TSP would be a stunning breakthrough ...