Solve Travelling Salesman Problem

Solve Travelling Salesman Problem-21
The traveling salesman problem is regarded as difficult to solve.If there is a way to break this problem into smaller component problems, the components will be at least as complex as the original one.Rules which would push the number of trials below the number of permutations of the given points, are not known.

The traveling salesman problem is regarded as difficult to solve.If there is a way to break this problem into smaller component problems, the components will be at least as complex as the original one.Rules which would push the number of trials below the number of permutations of the given points, are not known.

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Each city is connected to other close by cities, or nodes, by airplanes, or by road or railway.

Each of those links between the cities has one or more weights (or the cost) attached.

The result suggests that these simple lifeforms might actually offer an alternative processing method to conventional computers.

Or, to put it more simply, our state-of-the-art electronic devices could actually learn something from an amoeba. To be clear, the amoeba wasn't faster than computers, not by a long stretch (check out how slow they move in the video below).

The Traveling Salesman Problem is typical of a large class of "hard" optimization problems that have intrigued mathematicians and computer scientists for years.

Most important, it has applications in science and engineering.To make sure the amoeba entered the 'cities' in an optimal way, the researchers used light (which the amoeba doesn't like) to illuminate certain channels that were too far apart or that it had already visited, and to stop it from entering several channels simultaneously.To the team's astonishment, it didn't take exponentially longer for the amoeba to figure out a reasonable (nearly optimal) way to enter eight different channels than it did to enter four, despite the increase in the number of possible configurations."Interestingly," the team added, "the quality of the solution does not degrade despite the explosive expansion of the search space."To be fair, conventional computers are pretty slick, and they can also solve the problem in linear time as it gets exponentially harder.Menger defines the problem, considers the obvious brute-force algorithm, and observes the non-optimality of the nearest neighbour heuristic: We denote by messenger problem (since in practice this question should be solved by each postman, anyway also by many travelers) the task to find, for finitely many points whose pairwise distances are known, the shortest route connecting the points.Of course, this problem is solvable by finitely many trials. The traveling salesman problem was defined in the 1800s by the Irish mathematician W. Hamilton and by the British mathematician Thomas Kirkman. In this context, better solution often means a solution that is cheaper, shorter, or faster. It is most easily expressed as a graph describing the locations of a set of nodes.The Travelling Salesman Problem describes a salesman who must travel between N cities.The order in which he does so is something he does not care about, as long as he visits each once during his trip, and finishes where he was at first.This is what computer scientists call NP-hard problems. The easiest (and most expensive solution) is to simply try all possibilities.The problem with this is that for N cities you have (N-1) factorial possibilities.

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