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This paper proposes a learning-based approach to optimize the multiple traveling salesman problem (MTSP), which is one classic representative of cooperative combinatorial optimization problems. The MTSP is interesting to study, because the problem arises from numerous practical applications and efficient approaches to optimize the MTSP can potentially be adapted for other cooperative optimization problems. However, the MTSP is rarely researched in the deep learning domain because of certain difficulties, including the huge search space, the lack of training data that is labeled with optimal solutions and the lack of architectures that extract interactive behaviors among agents. This paper constructs an architecture consisting of a shared graph neural network and distributed policy networks to learn a common policy representation to produce near-optimal solutions for the MTSP. We use a reinforcement …