Travelling salesman problem Totally Explained

Everything about The Traveling Salesman totally explained

The traveling salesman problem (TSP) is a problem in discrete or combinatorial optimization.
It is a prominent illustration of a class of problems in computational complexity theory which are classified as NP-hard. Mathematical problems related to the traveling salesman problem were treated in the 1800s by the Irish mathematician Sir William Rowan Hamilton and by the British mathematician Thomas Kirkman. A discussion of the early work of Hamilton and Kirkman can be found in Graph Theory 1736-1936. 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 Menger. The problem was later undertaken by Hassler Whitney and Merrill M. Flood at Princeton. A detailed treatment of the connection between Menger and Whitney as well as the growth in the study of TSP can be found in Alexander Schrijver's 2005 paper "On the history of combinatorial optimization (till 1960)".

Problem statement

Given a number of cities and the costs of traveling from any city to any other city, what is the least-cost round-trip route that visits each city exactly once and then returns to the starting city? Observation: the size of the solution space is

frac+0.551

Further Information

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