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...

We present a map from the travelling salesman problem (TSP), prototypical NP-complete combinatorial optimisation task, to ground state associated with system of many-qudits. Conventionally, TSP is cast into quadratic unconstrained binary (QUBO) problem, that can be solved on an Ising machine. The size corresponding physical system's Hilbert space $2^{N^2}$, where $N$ number cities considered in...

The traveling salesman problem (TSP) is a well-known optimization problem in graph theory, as well as in operations research that has nowadays received much attention because of its practical applications in industrial and service problems. In this problem, a salesman starts to move from an arbitrary place called depot and after visits all of the nodes, finally comes back to the depot. The obje...

ABSTRACT: Travelling salesman problem (TSP) is a routing problem, which is a sub-problem of many application domains such as transportation, network communication. In this paper, we propose a novel methodology which solves the problem ACO algorithm has defined with well distribution strategy in which total search space area is partition into P numbers of hyper-cubic quadrants where P is the dim...

There exist a number of problem classes for which obtaining the exact solution becomes exponentially expensive with increasing problem size. The quadratic assignment problem (QAP) or the travelling salesman problem (TSP) are just two examples of such NP-hard problems. In practice, approximate algorithms are employed to obtain a suboptimal solution, where one must face a trade-off between comput...

We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to b...

We present and analyze a Self Organizing Feature Map (SOFM) for the NP-complete problem of the travelling salesman (TSP): finding the shortest closed path joining N cities. Since the SOFM has discrete input patterns (the cities of the TSP) one can examine its dynamics analytically. We show that, with a particular choice of the distance function for the net, the energy associated to the SOFM has...

The Travelling Salesman Problem or the TSP is a representative of a large class of problems known as combinatorial optimization problems. In the ordinary form of the TSP, a map of cities is given to the salesman and he has to visit all the cities only once to complete a tour such that the length of the tour is the shortest among all possible tours for this map. The data consist of weights assig...

The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...