Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning

2025-06-03

AI Summary

Neural combinatorial optimization (NCO) models exhibit poor cross-scale generalization on vehicle routing problems (CVRP/TSP)—models trained on small-scale instances (e.g., 100 nodes) fail dramatically on ultra-large-scale test instances (up to 10⁵ nodes). Method: This paper proposes the first large language model (LLM)-driven test-time projection learning framework. Without fine-tuning or retraining, it dynamically constructs a distribution-aligned latent-space projection during inference to calibrate scale- and structure-induced distribution shifts between training and testing regimes. Crucially, the LLM serves as an interpretable semantic orchestrator, jointly optimizing the projection operator and the NCO decoder. Results: A backbone model trained solely on 100-node instances achieves state-of-the-art performance on diverse 10⁵-node benchmarks—outperforming all baselines by significant margins. It demonstrates robust cross-scale generalization across three orders of magnitude, establishing the first purely inference-time solution for scalable, distribution-agnostic NCO.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Search and Optimization: Learning to Search
• Computer Vision: Large Vision Models

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on small-scale instances (e.g., 100 nodes), have demonstrated considerable success on problems of similar scale, their performance significantly degrades when applied to large-scale scenarios. This degradation arises from the distributional shift between training and testing data, rendering policies learned on small instances ineffective for larger problems. To overcome this limitation, we introduce a novel learning framework driven by Large Language Models (LLMs). This framework learns a projection between the training and testing distributions, which is then deployed to enhance the scalability of the NCO model. Notably, unlike prevailing techniques that necessitate joint training with the neural network, our approach operates exclusively during the inference phase, obviating the need for model retraining. Extensive experiments demonstrate that our method enables a backbone model (trained on 100-node instances) to achieve superior performance on large-scale Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) of up to 100K nodes from diverse distributions.

Problem

• Addresses performance drop in Neural Combinatorial Optimization for large-scale VRPs
• Overcomes distributional shift between small training and large testing instances
• Enhances NCO scalability via test-time projection learning without retraining

Innovation

• Uses LLMs to project training-test distributions
• Enhances NCO scalability without retraining
• Achieves performance on 100K-node VRPs