travelling salesman problem


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travelling salesman problem

(algorithm, complexity)
(TSP or "shortest path", US: "traveling") Given a set of towns and the distances between them, determine the shortest path starting from a given town, passing through all the other towns and returning to the first town.

This is a famous problem with a variety of solutions of varying complexity and efficiency. The simplest solution (the brute force approach) generates all possible routes and takes the shortest. This becomes impractical as the number of towns, N, increases since the number of possible routes is !(N-1). A more intelligent algorithm (similar to iterative deepening) considers the shortest path to each town which can be reached in one hop, then two hops, and so on until all towns have been visited. At each stage the algorithm maintains a "frontier" of reachable towns along with the shortest route to each. It then expands this frontier by one hop each time.

Pablo Moscato's TSP bibliography. Fractals and the TSP.
References in periodicals archive ?
Zhang, "Swarm simulated annealing algorithm with knowledge-based sampling for travelling salesman problem," International Journal of Intelligent Systems Technologies and Applications, vol.
Braun, "On solving travelling salesman problems by genetic algorithms," in Parallel Problem Solving from Nature: 1st Workshop, PPSN I Dortmund, FRG, October 1-3, 1990 Proceedings, vol.
Table II: Computational results for the Travelling Salesman Problem with [alpha] = 0.
For showing the efficiency of SimSum1, the algorithm was tested over several well-known combinatorial problems like Dynamic Facility Layout Problem, Travelling Salesman Problem and Graph Labelling Problem.
And within the MTSP it is the fixed destination multiple depot multiple travelling salesman problem (MDMTSP), but the solutions in the literature did not mention the additional sub tour construction.
In our case the travelling salesman problem (TSP) was approached with the self-organizing network by the elastic tape method.
This paper mapped FSPs and all kinds of constraint mechanisms to travelling salesman problems (TSPs), through which a large volume of achievements concerning TSP model and its algorithm is obtained (Wang, 2012; Tapan et al.