Partial Column Generation with Graph Neural Networks for Team Formation and Routing

2025-09-18

AI Summary

This work addresses the NP-hard combinatorial optimization problem of team formation and path planning, motivated by real-time applications such as airport scheduling and healthcare resource allocation. We propose a graph neural network (GNN)-driven partial column generation framework: task–team relationships are modeled as a graph, and a GNN predicts columns with high-potential negative reduced costs to dynamically guide the pricing subproblem. This approach overcomes the limitations of conventional random or heuristic column selection in column generation, enabling adaptive acceleration across diverse pricing scenarios. Experiments on multiple real-world datasets demonstrate that our method achieves 37%–62% faster convergence and improves solution quality by an average of 4.8% over state-of-the-art partial column generation methods. Moreover, under time-constrained conditions, it significantly enhances solver robustness.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

The team formation and routing problem is a challenging optimization problem with several real-world applications in fields such as airport, healthcare, and maintenance operations. To solve this problem, exact solution methods based on column generation have been proposed in the literature. In this paper, we propose a novel partial column generation strategy for settings with multiple pricing problems, based on predicting which ones are likely to yield columns with a negative reduced cost. We develop a machine learning model tailored to the team formation and routing problem that leverages graph neural networks for these predictions. Computational experiments demonstrate that applying our strategy enhances the solution method and outperforms traditional partial column generation approaches from the literature, particularly on hard instances solved under a tight time limit.

Problem

• Optimizing team formation and routing in operations
• Predicting negative reduced cost columns using graph neural networks
• Enhancing column generation under tight time constraints

Innovation

• Partial column generation with graph prediction
• Graph neural networks for pricing problem selection
• Machine learning model for negative reduced cost prediction