Traveling Salesman Problem

Given a set of cities and distance between every pair of cities the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point. Travelling salesman problem is the most notorious computational problem.

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It is most easily expressed as a graph describing the locations of a set of nodes.

Traveling salesman problem. The problem is to find a path that visits each city once returns to the starting city and minimizes the distance traveled. The travelling salesman problem was mathematically formulated in the 1800s by the irish mathematician w r. Hamilton and by the british mathematician thomas kirkman hamilton s icosian game was a recreational puzzle based on finding a hamiltonian cycle.

The traveling salesman problem is a problem in graph theory requiring the most efficient i e least total distance hamiltonian cycle a salesman can take through each of cities. The wolfram language command findshortesttour g attempts to find a shortest tour which is a hamiltonian cycle with. The hamiltoninan cycle problem is to find if there exist a tour that visits every city exactly once.

No general method of solution is known and the problem is np hard. The general form of the tsp appears to have been first studied by mathematicians during the 1930s in vienna and at harvard notably by karl. We can use brute force approach to evaluate every possible tour and select the best one.

The traveling salesman problem often called tsp is a classic algorithmic problem in the field of computer science and operations research it is focused on optimization in this context better solution often means a solution that is cheaper shorter or faster tsp is a mathematical problem. Note the difference between hamiltonian cycle and tsp. For n number of vertices in a graph there are n 1.

Travelling salesman problem tsp. Traveling salesman problem an optimization problem in graph theory in which the nodes cities of a graph are connected by directed edges routes where the weight of an edge indicates the distance between two cities.

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