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This paper introduces CARSS (Cooperative Attention-guided ReinforcementSubpath Synthesis), a novel approach to address the Traveling Salesman Problem(TSP) by leveraging cooperative Multi-Agent Reinforcement Learning (MARL).CARSS decomposes the TSP solving process into two distinct yet synergisticsteps: "subpath generation" and "subpath merging." In the former, a cooperativeMARL framework is employed to iteratively generate subpaths using multipleagents. In the latter, these subpaths are progressively merged to form acomplete cycle. The algorithm's primary objective is to enhance efficiency interms of training memory consumption, testing time, and scalability, throughthe adoption of a multi-agent divide and conquer paradigm. Notably, attentionmechanisms play a pivotal role in feature embedding and parameterizationstrategies within CARSS. The training of the model is facilitated by theindependent REINFORCE algorithm. Empirical experiments reveal CARSS'ssuperiority compared to single-agent alternatives: it demonstrates reduced GPUmemory utilization, accommodates training graphs nearly 2.5 times larger, andexhibits the potential for scaling to even more extensive problem sizes.Furthermore, CARSS substantially reduces testing time and optimization gaps byapproximately 50% for TSP instances of up to 1000 vertices, when compared tostandard decoding methods.

CARSS: Cooperative Attention-guided Reinforcement Subpath Synthesis for Solving Traveling Salesman Problem