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...

The free clustered travelling salesman problem (FCTSP) is an extension of the classical travelling salesman problem where the set of vertices is partitioned into clusters, and the task is to find a minimum cost Hamiltonian tour such that the vertices in any cluster are visited contiguously. This paper proposes the use of a memetic algorithm (MA) that combines the global search ability of Geneti...

Ant Colony optimization has proved suitable to solve a wide range of combinatorial optimization (or NP-hard) problems as the Travelling Salesman Problem (TSP). The first step of ACO algorithm is to set the parameters that drive the algorithm. The parameter has an important impact on the performance of the ant colony algorithm. The basic parameters that are used in ACO algorithms are; the relati...

In the Euclidean traveling salesman and buyers problem (TSBP), we are given a set of convex regions in d-dimensional space, and we wish to nd a minimum-cost tour that visits all the regions. The cost of a tour depends on the length of the tour itself and on the distance that buyers within each region need to travel to meet the salesman. We show that constantfactor approximations to the TSBP and...

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