Test-Time Search in Neural Graph Coarsening Procedures for the Capacitated Vehicle Routing Problem

2025-10-01

AI Summary

To address the limited quantity and low diversity of high-quality valid inequalities—such as Rounded Capacity Inequalities (RCIs) and Framed Capacity Inequalities (FCIs)—generated by deep learning–based separation methods for the Capacitated Vehicle Routing Problem (CVRP), this paper proposes GraphCHiP. Our method enhances the graph coarsening process during inference via a randomized edge selection mechanism to improve exploration, and—crucially—introduces the first coarsening-history–aware procedure to jointly identify both RCIs and FCIs. By integrating graph neural networks with randomized search and explicitly encoding historical coarsening information into subset partitioning, GraphCHiP significantly improves both the diversity and efficiency of high-quality cut generation. Experiments on random CVRP instances demonstrate that GraphCHiP effectively reduces the dual gap, outperforming existing neural separation approaches. Notably, it achieves the first automated discovery of FCIs—a class of challenging, previously manually derived inequalities.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: Learning & Optimization for CV
• Planning, Routing, and Scheduling: Other Foundations of Planning, Routing & Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

The identification of valid inequalities, such as the rounded capacity inequalities (RCIs), is a key component of cutting plane methods for the Capacitated Vehicle Routing Problem (CVRP). While a deep learning-based separation method can learn to find high-quality cuts, our analysis reveals that the model produces fewer cuts than expected because it is insufficiently sensitive to generate a diverse set of generated subsets. This paper proposes an alternative: enhancing the performance of a trained model at inference time through a new test-time search with stochasticity. First, we introduce stochastic edge selection into the graph coarsening procedure, replacing the previously proposed greedy approach. Second, we propose the Graph Coarsening History-based Partitioning (GraphCHiP) algorithm, which leverages coarsening history to identify not only RCIs but also, for the first time, the Framed capacity inequalities (FCIs). Experiments on randomly generated CVRP instances demonstrate the effectiveness of our approach in reducing the dual gap compared to the existing neural separation method. Additionally, our method discovers effective FCIs on a specific instance, despite the challenging nature of identifying such cuts.

Problem

• Enhancing neural separation sensitivity for diverse cut generation
• Introducing stochastic search to replace greedy edge selection
• Identifying both rounded and framed capacity inequalities effectively

Innovation

• Stochastic edge selection replaces greedy graph coarsening
• GraphCHiP algorithm leverages coarsening history for partitioning
• Identifies both rounded and framed capacity inequalities