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In this paper, we provide a novel strategy for solving Traveling SalesmanProblem, which is a famous combinatorial optimization problem studied intenselyin the TCS community. In particular, we consider the imitation learningframework, which helps a deterministic algorithm making good choices wheneverit needs to, resulting in a speed up while maintaining the exactness of thesolution without suffering from the unpredictability and a potential largedeviation.  Furthermore, we demonstrate a strong generalization ability of a graph neuralnetwork trained under the imitation learning framework. Specifically, the modelis capable of solving a large instance of TSP faster than the baseline whilehas only seen small TSP instances when training.

Travel the Same Path: A Novel TSP Solving Strategy