Probing Neural TSP Representations for Prescriptive Decision Support

2026-02-06

AI Summary

This study investigates whether neural solvers for the Traveling Salesman Problem (TSP) learn transferable internal representations that can support real-world logistics decision-making tasks beyond route construction, such as critical node removal and essential edge preservation analysis. For the first time, we treat attention-based neural TSP solvers as general-purpose encoders, extracting their learned embeddings and transferring them via probing models to two NP-hard prescriptive downstream tasks that assess the sensitivity of solution quality to individual nodes or edges. Experimental results demonstrate that stronger TSP solvers yield more effective transferable representations. On TSP100 instances, the probing models achieve top-1 accuracies of 65% and 73% on critical node and critical edge identification tasks, respectively, significantly outperforming baseline methods (58% and 67%).

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The field of neural combinatorial optimization (NCO) trains neural policies to solve NP-hard problems such as the traveling salesperson problem (TSP). We ask whether, beyond producing good tours, a trained TSP solver learns internal representations that transfer to other optimization-relevant objectives, in the spirit of transfer learning from other domains. We train several attention-based TSP policies, collect their internal activations, and train probes on node/edge embeddings for two NP-hard prescriptive downstream tasks inspired by real-world logistics scenarios: node-removal sensitivity (identifying the most impactful node to remove) and edge-forbid sensitivity (identifying the most critical edge to retain). On a Euclidean TSP100-trained model, probes for both tasks are competitive with existing baselines. Ensembling probe signals with geometric features outperforms the strongest baselines: 65\% top-1 accuracy (vs. 58\% baseline) for the best-node-removal task, and 73\% top-1 accuracy (vs. 67\% baseline) for the worst-edge identification task. To our knowledge, we are the first to study neural TSP solvers as transferable encoders for prescriptive what-if decision-support objectives beyond tour construction. Finally, we show that transfer accuracy increases with solver quality across training and model scale, suggesting that training stronger NCO solvers also yields more useful encoders for downstream objectives. Our code is available at: github.com/ReubenNarad/tsp_prescriptive_probe

Problem

• neural combinatorial optimization
• traveling salesperson problem
• transfer learning
• prescriptive decision support
• what-if analysis

Innovation

• neural combinatorial optimization
• transfer learning
• probing
• prescriptive decision support
• traveling salesperson problem