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 polynomial-cost unconstrained combinatorial optimization problems. This paper proposes a new framework, called HypOp, which greatly advances the state of the art for solving combinatorial optimization problems in several aspects: (i) it generalizes the prior results to constrained optimization problems with an arbitrary cost function; (ii) it broadens the application to higher dimensional problems by leveraging a hypergraph neural network structure; (iii) it enables scalability to much larger problems by introducing a new distributed and parallel architecture for hypergraph neural network training; (iv) it demonstrates generalizability to other problem formulations by knowledge transfer from the learned experience of addressing one set of cost/constraints to another set for the same hypergraph; (v) it significantly boosts the solution accuracy compared with the prior art by suggesting a fine-tuning step using simulated annealing; (vi) HypOp shows a remarkable progress on benchmark examples, with run times improved by up to fivefold using a combination of fine-tuning and distributed training techniques. The framework allows addressing a novel set of scientific problems including hypergraph MaxCut problem, satisfiability problems (3SAT), and resource allocation. We showcase the application of HypOp in scientific discovery by solving a hypergraph MaxCut problem on the NDC drug-substance hypergraph. Through extensive experimentation on a variety of combinatorial optimization problems, HypOp demonstrates superiority over existing unsupervised learning-based solvers and generic optimization methods.

翻译：高维约束组合优化问题的可扩展求解是多个科学与工程学科面临的挑战。近期研究开创性地应用图神经网络解决多项式代价无约束组合优化问题。本文提出名为HypOp的新框架，从多个维度显著推进了组合优化问题求解的技术水平：(i) 将先前成果推广至具有任意代价函数的约束优化问题；(ii) 通过引入超图神经网络结构扩展至高维问题；(iii) 提出分布式并行超图神经网络训练架构，实现更大规模问题的可扩展性；(iv) 通过将解决某组代价/约束问题的学习经验迁移至同一超图的其他问题形式，展现泛化能力；(v) 引入模拟退火微调步骤，相较现有技术显著提升求解精度；(vi) HypOp在基准测试中取得突破性进展，通过微调与分布式训练技术组合可实现高达五倍的运行时间优化。该框架支持解决包括超图最大割问题、可满足性问题(3SAT)及资源分配在内的新型科学问题。我们通过在NDC药物-物质超图上求解超图最大割问题，展示了HypOp在科学发现中的应用。通过多种组合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及通用优化方法的优越性能。