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A salesman wants to visit all cities,A, B, C and D. What is the best way to do this (cheapest airline tickets, and minimal travel time)?

Optimal route of a salesman visiting the 15 biggest cities in Germany. The route shown is the shortest of the 43,589,145,600 possible ones.

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

William Rowan Hamilton