# The Travelling Salesman Problem

Decent Essays

Travelling Salesman Problem
Institution
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Introduction
A salesman is required to visit all the cities with a known distance between every two cities keeping in mind that the cities have to be visited once. The problem facing the salesman is to determine the shortest possible route the salesman has to use to visit the towns just once and goes back to the original city.
The Travelling Salesman Problem first statement was made by a Viennese mathematician Karl Menger. It brought a connection and relation with the definition of the curve length proposed by Menger that stated that the stretch of a curves’ distance can be defined as the lower limit upper bound of the groups of all numbers that can be contained by taking each group of points of the curve and producing the shortest length of the polygonal graph. This problem is called the messenger problem.
The Travelling Salesman Problem can be stated as where a network has n cities or nodes, and one of the nodes (node 1) is the origin and the cost of travelling which include the …show more content…

No one has come up with the efficient way of coming up with the solution to large size problems as the NP-complete problems are much intractable.
The exact methods provide an exact optimal solution to the problem. One of the ways of solving the Travelling Salesman Problem is simply taking all the available and feasible solutions and evaluating their function values and selecting the best out of the solutions. The process might be inefficient, impractical and time-consuming due to a large number of a possible solution that applies to the problem. Travelling Salesman Problem focuses on getting the heuristically good solution to the problem within a short period.
The solution to the problem can be obtained by carrying numerous trials in the given cities less than their