Adapter-based Cross-problem Knowledge Transfer for Traveling Salesman Problems

This paper proposes an adapter-based lightweight transfer learning method integrated with Low-Rank Adaptation (LoRA) to address combinatorial optimization challenges in complex variants of the Traveling Salesman Problem (TSP), such as the Multiple TSP and the Colored TSP. To tackle the limitations of existing neural combinatorial optimization methods, including model redundancy and insufficient cross-problem knowledge transfer capabilities, we design a pre-training and fine-tuning paradigm. Specifically, a Transformer-based general TSP solver is first pre-trained. Subsequently, by freezing the parameters of the backbone network and introducing lightweight adapter modules (Adapter-LoRA), efficient knowledge transfer to MTSP and CTSP is achieved. Through the synergistic optimization of low-rank matrix update strategies and problem-specific modules, the proposed method retains the spatial encoding capabilities of the pre-trained model while significantly reducing trainable parameters for downstream tasks (by 70%). Experimental results demonstrate that, compared to baseline methods trained from scratch, the proposed approach maintains a solution quality gap of <1% for MTSP/CTSP instances with 20 and 50 nodes, while achieving faster convergence speed and lower memory consumption.