A reinforcement learning approach for optimizing multiple traveling salesman problems over graphs

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 learning approach to train the model, overcoming the requirement data labeled with ground truth. We use a two-stage approach, where reinforcement learning is used to learn an allocation of agents to vertices, and a regular optimization method is used to solve the single-agent traveling salesman problems associated with each agent. We introduce a S-samples batch training method to reduce the variance of the gradient, improving the performance significantly. Experiments demonstrate our approach successfully learns a strong policy representation that outperforms integer linear programming and heuristic algorithms, especially on large scale problems. (C) 2020 Elsevier B.V. All rights reserved.