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 presents a constraint logic programming model for the traveling salesman problem with time windows which yields an exact branch-and-bound optimization algorithm without any restrictive ...

The travelling salesman problem (TSP) remains one of the most challenging NP‐hard problems in combinatorial optimisation, with significant implications for logistics, network design and route planning ...

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 ...

We have found the best path to take between the stars. The travelling salesman problem, an infamous mathematical puzzle that seeks the shortest route between many locations while visiting each only ...