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How do you solve the traveling salesman problem?

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Quick Answer

According to Joe Malkevitch of York College and the American Mathematical Society, the traveling salesman problem can be solved using algorithms. However, attempts to find a simple algorithm to answer the traveling salesman problem have failed.

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According to Joe Malkevitch, the traveling salesman problem involves a hypothetical salesman starting from his home, making his rounds to sell his goods and then returning home. The problem for the salesman is to take the route that costs the least, called the minimal cost tour or the optimal tour. The traveling salesman problem appeared in mathematics as early as 1832, when it was referenced as a practical problem in a German book. Karl Menger is credited with popularizing the problem in the European mathematical community in the 1920s, and Merrill Flood popularized it in the United States. Flood also introduced the problem to the Rand Corporation, which was involved in operations research; the Rand Corporation attempted to solve the problem with operations research.

The traveling salesman problem is relevant to modern business, according to Malkevitch. Just like a salesman trying to find the optimal route to take, companies attempt to find the cheapest and easiest routes by which to sell their products. A company that manufactures computer chips could save money using an optimal route.

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