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Traveling Salesman Problem
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The Traveling Salesman Problem is one of the most well known problems in operations research, computer science, and mathematics. The basic idea is basically trying to find the shortest cycle in a network such that all the nodes are visited and the minimum total distance is traveled. A more "technical" definition follows (Golden, Bodin, Doyle, Stewart, 1980):
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The difficulty with the Traveling Salesman Problem is that every city can only be used once in a tour. If the letters in the above example represented cities, this child tours created by this crossover operation would be invalid. Child 1 goes to city F & B twice, and never goes to cities D or E.
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Abstract: The Traveling Salesman Problem (TSP) is computationally expensive to evaluate. It can... be readily decomposed into subproblems that can be computed in parallel. Developing a distributed program taking advantage of such a decomposition, however, remains a difficult problem.
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The Traveling Salesman Problem (TSP) seems simple. However, finding the solution can be difficult, even for a small number of points. Highly specialized software, based on mathematical and scientific principles, is required.
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The Traveling Salesman Problem (TSP) is not hard to explain. For a given set of cites, visit each city once (once and only once) and minimize the distance you travel. This deceptively simple problem is trivial given a small set of cities... as you add more cities the number of possible paths goes through the roof. It should come as no surprise that the TSP is classified as an NP-Hard problem, with the number of Hamiltonian paths being equal to n!/2 where n is equal to the number of cities in the problem.
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The Traveling Salesman Problem is to find the shortest circuitous path connecting N cities (meaning that a traveling salesman following that path would visit each city only once). Although it can in principle be solved by brute force (by calculating the length of every possible circuit), this is not practical because the number of circuits grows so fast that even for N = 25 cities, it would take longer than the age of the universe (~10 billion years) to check every path, at a rate of one million paths per second!
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Traveling Salesman Problem