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The Concorde TSP Solver is a program for solving the travelling salesman problem. It was written by David Applegate , Robert E. Bixby , Vašek Chvátal , and William J. Cook , in ANSI C , and is freely available for academic use.
Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
The algorithm builds a tour for the traveling salesman one edge at a time and thus maintains multiple tour fragments, each of which is a simple path in the complete graph of cities. At each stage, the algorithm selects the edge of minimal cost that either creates a new fragment, extends one of the existing paths or creates a cycle of length ...
This algorithm is no longer the best polynomial time approximation algorithm for the TSP on general metric spaces. Karlin, Klein, and Gharan introduced a randomized approximation algorithm with approximation ratio 1.5 − 10 −36. It follows similar principles to Christofides' algorithm, but uses a randomly chosen tree from a carefully chosen ...
2-opt. In optimization, 2-opt is a simple local search algorithm for solving the traveling salesman problem.The 2-opt algorithm was first proposed by Croes in 1958, [1] although the basic move had already been suggested by Flood. [2]
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In the worst case, the algorithm results in a tour that is much longer than the optimal tour. To be precise, for every constant r there is an instance of the traveling salesman problem such that the length of the tour computed by the nearest neighbour algorithm is greater than r times the length of the optimal tour. Moreover, for each number of ...