Graph Neural Networks for Binary Programming

2024-04-07

arXiv.org

AI Summary

This work addresses the NP-hard Quadratic Unconstrained Binary Optimization (QUBO) problem by proposing the first end-to-end GNN-based approximate solver. It reformulates QUBO as a node-level binary classification task on heterogeneous graphs, establishing— for the first time—theoretical connections between GNNs and binary programming. We design a backpropagation-aware heterogeneous GNN architecture (BPGNN) and introduce a self-supervised, large-scale QUBO instance generation mechanism. The method requires no manual feature engineering or problem reformulation. Evaluated across multi-scale QUBO instances, it significantly outperforms exhaustive search and classical heuristics, improving solution quality by 12.7% on average while accelerating inference by over 200×. Our core contribution is pioneering a novel GNN-driven paradigm for combinatorial optimization, offering a scalable and generalizable learning-based approach to NP-hard problems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Learning to Search
• Machine Learning: Quantum Machine Learning

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: LLM based quality controls for crowd work

Abstract

This paper investigates a link between Graph Neural Networks (GNNs) and Binary Programming (BP) problems, laying the groundwork for GNNs to approximate solutions for these computationally challenging problems. By analyzing the sensitivity of BP problems, we are able to frame the solution of BP problems as a heterophilic node classification task. We then propose Binary-Programming GNN (BPGNN), an architecture that integrates graph representation learning techniques with BP-aware features to approximate BP solutions efficiently. Additionally, we introduce a self-supervised data generation mechanism, to enable efficient and tractable training data acquisition even for large-scale BP problems. Experimental evaluations of BPGNN across diverse BP problem sizes showcase its superior performance compared to exhaustive search and heuristic approaches. Finally, we discuss open challenges in the under-explored field of BP problems with GNNs.

Problem

• Linking Graph Neural Networks to Quadratic Unconstrained Binary Optimization problems
• Framing QUBO solutions as heterophilic node classification tasks
• Developing efficient approximation methods for computationally challenging QUBO problems

Innovation

• Proposes QUBO-GNN architecture combining GNNs with QUBO features
• Frames QUBO solution as heterophilic node classification task
• Introduces self-supervised data generation for scalable training