# The Traveling Salesman Problem 1: Optimal Paths

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A salesman, starting from his home city, needs to visit every city on his route exactly once and finally return home. As there are only a finite number of possibilities, it is plausible for him to select the visiting order so that the total distance traveled in his tour is as small as possible. All the data he needs is to know for each pair of cities the distance from one to the other.

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Contributed by: Jaime Rangel-Mondragon (July 2012)

Open content licensed under CC BY-NC-SA

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Reference

[1] E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys, eds., *The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization*, New York: John Wiley & Sons, 1985.

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