Scalable addressing of high dimensional constrained combinatorial optimization problems is a challenge that arises in several science and engineering disciplines. Recent work introduced novel application of graph neural networks for solving quadratic-cost combinatorial optimization problems. However, effective utilization of models such as graph neural networks to address general problems with higher order constraints is an unresolved challenge. This paper presents a framework, HypOp, which advances the state of the art for solving combinatorial optimization problems in several aspects: (i) it generalizes the prior results to higher order constrained problems with arbitrary cost functions by leveraging hypergraph neural networks; (ii) enables scalability to larger problems by introducing a new distributed and parallel training architecture; (iii) demonstrates generalizability across different problem formulations by transferring knowledge within the same hypergraph; (iv) substantially boosts the solution accuracy compared with the prior art by suggesting a fine-tuning step using simulated annealing; (v) shows a remarkable progress on numerous benchmark examples, including hypergraph MaxCut, satisfiability, and resource allocation problems, with notable run time improvements using a combination of fine-tuning and distributed training techniques. We showcase the application of HypOp in scientific discovery by solving a hypergraph MaxCut problem on NDC drug-substance hypergraph. Through extensive experimentation on various optimization problems, HypOp demonstrates superiority over existing unsupervised learning-based solvers and generic optimization methods.

翻译：可扩展地解决高维约束组合优化问题是多个科学与工程学科面临的挑战。近期研究引入了图神经网络在二次成本组合优化问题中的创新应用。然而，有效利用图神经网络等模型解决具有高阶约束的通用问题仍是一个未解决的挑战。本文提出HypOp框架，从多个方面推动了组合优化问题求解的现有技术发展：（i）通过利用超图神经网络，将先验结果推广至具有任意成本函数的高阶约束问题；（ii）引入新型分布式并行训练架构，实现对更大规模问题的可扩展性；（iii）通过在同一超图内迁移知识，展示了跨不同问题形式的泛化能力；（iv）提出基于模拟退火的微调步骤，显著提升了相较于现有技术的解精度；（v）在超图MaxCut、可满足性问题和资源分配问题等多个基准示例上取得了显著进展，通过微调与分布式训练技术的结合实现了运行时间的显著改善。我们通过在NDC药物-物质超图上求解超图MaxCut问题，展示了HypOp在科学发现中的应用。通过对各类优化问题的广泛实验，HypOp展现出超越现有无监督学习求解器和通用优化方法的优越性能。