🤖 AI Summary
This work addresses the limited cross-scale and cross-distribution generalization of non-autoregressive neural solvers for the Traveling Salesman Problem (TSP), which stems from insufficient geometric inductive bias and unstable training signals. To overcome these limitations, the authors propose GeoRouteNet, a novel architecture that enhances geometric representation through centralized node features, learnable radial distance basis functions, and a distance-aware graph attention mechanism. Training stability is further improved via Multi-Candidate Self-comparative Reinforcement Learning (MCS-RL). The model achieves state-of-the-art optimality gaps of 0.32% and 1.26% on TSP50 and TSP100, respectively, and reduces the average optimality gap on TSPLIB EUC_2D instances from 17.12% to 3.60%. Moreover, GeoRouteNet demonstrates significantly higher batch inference throughput compared to Concorde and LKH3.
📝 Abstract
The traveling salesman problem (TSP) is a canonical NP-hard combinatorial optimization benchmark that tests the representational capacity and generalization of neural solvers. While non-autoregressive (NAR) approaches offer parallel inference, they often lack sufficient geometric inductive bias and stable training signals, leading to degraded performance under cross-scale and cross-distribution shifts. We propose GeoRouteNet, a geometry-enhanced NAR neural solver for Euclidean TSP. On the model side, GeoRouteNet incorporates centered node features, learnable radial distance basis functions, distance-aware graph attention with explicit edge messaging, LayerNorm-SwiGLU feed-forward blocks, and cross-layer attentive residual mixing. On the training side, we design multi-candidate self-comparison reinforcement learning (MCS-RL), which samples multiple candidate tours per instance, constructs adaptive baselines from greedy and peer candidates, and adds winner-candidate guidance with annealed entropy regularization. On 10,000 random TSP50 instances, GeoRouteNet achieves a 0.32% optimality gap under Beam-1000 decoding. On TSP100, the gap is 1.26%. On 27 stratified TSPLIB EUC_2D instances, the overall gap drops from 17.12% (NAR4TSP reproduction) to 3.60%, while batch inference throughput substantially exceeds that of Concorde and LKH3. Ablation studies confirm that geometric structure enhancement and multi-candidate training are complementary: structure improvements dominate cross-distribution gains, while MCS-RL further stabilizes solution quality when paired with a strong geometric encoder.