基于图神经网络的二次二进制优化
Quadratic Binary Optimization with Graph Neural Networks
AI总结：
该研究探索图神经网络（GNNs）与二次无约束二进制优化（QUBO）的联系，提出QUBO-GNN架构并结合自监督数据生成机制，高效近似求解QUBO问题，性能优于传统方法。
摘要：
我们研究了图神经网络（GNNs）与二次无约束二进制优化（QUBO）问题之间的联系，为GNNs近似解决这些计算挑战性任务奠定基础。通过分析QUBO公式的敏感性，我们将QUBO问题的求解构建为异质性节点分类任务。然后我们提出QUBO-GNN架构，该架构整合图表示学习技术与QUBO感知特征，以高效近似求解。此外，我们引入自监督数据生成机制，即使对于大规模QUBO实例也能实现高效且可扩展的训练数据获取。QUBO-GNN在不同QUBO问题规模上的实验评估表明，其性能优于穷举搜索和启发式方法。最后，我们讨论了QUBO优化与基于GNN的学习交叉领域的开放挑战。
英文摘要：
We investigate a link between Graph Neural Networks (GNNs) and Quadratic Unconstrained Binary Optimization (QUBO) problems, laying the groundwork for GNNs to approximate solutions for these computationally challenging tasks. By analyzing the sensitivity of QUBO formulations, we frame the solution of QUBO problems as a heterophilic node classification task. We then propose QUBO-GNN, an architecture that integrates graph representation learning techniques with QUBO-aware features to approximate solutions efficiently. Additionally, we introduce a self-supervised data generation mechanism to enable efficient and scalable training data acquisition even for large-scale QUBO instances. Experimental evaluations of QUBO-GNN across diverse QUBO problem sizes demonstrate its superior performance compared to exhaustive search and heuristic methods. Finally, we discuss open challenges in the emerging intersection between QUBO optimization and GNN-based learning.
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