Title: Efficiently Solving the TSP in One-Shot Without Post-Processing
Primary area: learning on graphs and other geometries & topologies
Keywords: Travelling Salesman Problem, TSP, Neural Combinatorial Optimization

Abstract: Neural approaches relying on autoregressive (AR) solution construction for solving the Travelling Salesman Problem (TSP) — a cornerstone challenge in Combinatorial Optimization (CO) — can be computationally expensive during both training and inference, as each step of the solution construction requires a pass through the neural network. While non-autoregressive (NAR) methods promise efficient solution generation in just a single pass through the network, prior works have often required post-processing search techniques such as Monte Carlo Tree Search (MCTS), active search, beam search and 2-opt to achieve near-optimal performance. However, these techniques not only inflate inference times but have also drawn criticism for potentially overshadowing the model's intrinsic capability and raised questions about the contribution of the neural component in the solution generation pipeline.

To address these concerns, we demonstrate that high-quality solutions can be generated in one-shot using the NAR approach by producing highly accurate heatmaps without requiring sophisticated post-processing techniques. During inference, we decode the tour by selecting the top two edges per node based on the heatmap — a process which can be performed in parallel. Unlike most prior NAR approaches, which depend on costly expert solutions for supervised learning, our approach is trained with Self-Improvement Learning (SIL) which is entirely unsupervised. Trained as a unified model across graph sizes, our approach achieves near-optimal results. In addition, we introduce new metrics quantifying edge prediction precision and tour validity in the NAR setting, which emphasize the model's raw capabilities.

TL;DR: An efficient non-autoregressive neural method trained with unsupervised self-improvement learning that can generate near-optimal solutions for the TSP in one shot through accurate heatmaps without relying on costly post-processing