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

TL;DR

This paper presents a novel test-time projection learning framework using Large Language Models to improve the scalability and generalization of neural combinatorial optimization models for large-scale vehicle routing problems, without retraining.

Contribution

Introduces a test-time projection learning method driven by LLMs that enhances NCO model performance on large-scale VRPs without additional training.

Findings

Achieves superior performance on large-scale TSP and CVRP instances up to 100K nodes.

Operates solely during inference, avoiding retraining of the neural network.

Effectively mitigates distributional shift between training and testing data.

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.