The travelling salesman problem (TSP) is a whereby finite number of nodes are supposed to be visited exactly once, one after the other, in such way that total weight connecting arcs used visit these minimized. We propose labelling method solve TSP problem. algorithm terminates K−1 iterations, where K network. algorithm’s design allows it determine alternative tours if there any computational co...

In the travelling salesman problem (TSP), a travelling salesman completes a tour of “n” number of cities by stopping once in each city and completes the tour by returning to his starting point, while minimizing the distance and the cost. The asymmetric travelling salesman problem (ATSP) is the problem in which the cost of travel from city A to B is different from that from B to A. Marriage in H...

The Steiner Travelling Salesman Problem (STSP) is a variant of the TSP that is suitable for instances defined on road networks. We consider an extension of the STSP in which the road traversal costs are both stochastic and correlated. This happens, for example, when vehicles are prone to delays due to rush hours, road works or accidents. Following the work of Markowitz on portfolio selection, w...

This paper considers a version of the traveling salesman problem where the cities are to be visited multiple times. Each city has its own required number of visits. We investigate how the optimal solution and its objective value change when the numbers of visits are increased by a common multiplicator. In addition, we derive lower bounds on values of the multiplicator beyond which further incre...