最適性の指標に基づく隣接都市グラフを用いたTSPの解法

概要

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Using the characteristics of the optima is so effective to solve the traveling salesman problems. In our study, the edges on the optimal tours calculated completely have been analyzed to have the characteristics of their mutual relationship. The edge set based on the characteristics can construct the sub graph including all or almost the edges selected as optimal edges. If a sub graph has all or almost the edges of constructing the optimum, the investigation on this graph will lead to discover a good solution in reasonable time. Therefore, such sub graphs are the effective tools for existing methods to become improved methods. In this paper, Delaunay graph and two graphs, called Fragmented Nearest Neighbor graph, are proposed as the special sub graphs. And the experiments by the simulated annealing method that is executable on sub graph explain that Delaunay graph as a triangulated graph is the most effective graph among the three sub graphs to find optimum or sub optimum tour of the traveling salesman problems.