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

This paper introduces CARSS (Cooperative Attention-guided Reinforcement Subpath 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 synergistic steps: "subpath generation" and "subpath merging." In the former, a cooperative MARL framework is employed to iteratively generate subpaths using multiple agents. In the latter, these subpaths are progressively merged to form a complete cycle. The algorithm's primary objective is to enhance efficiency in terms of training memory consumption, testing time, and scalability, through the adoption of a multi-agent divide and conquer paradigm. Notably, attention mechanisms play a pivotal role in feature embedding and parameterization strategies within CARSS. The training of the model is facilitated by the independent REINFORCE algorithm. Empirical experiments reveal CARSS's superiority compared to single-agent alternatives: it demonstrates reduced GPU memory utilization, accommodates training graphs nearly 2.5 times larger, and exhibits the potential for scaling to even more extensive problem sizes. Furthermore, CARSS substantially reduces testing time and optimization gaps by approximately 50% for TSP instances of up to 1000 vertices, when compared to standard decoding methods.