Distributed constrained combinatorial optimization leveraging hypergraph neural networks

Scalable addressing of high-dimensional constrained combinatorial optimization problems is a challenge that arises in several science and engineering disciplines. Recent work introduced novel applications 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, that advances the state of the art for solving combinatorial optimization problems in several aspects: (1) it generalizes the prior results to higher-order constrained problems with arbitrary cost functions by leveraging hypergraph neural networks; (2) it enables scalability to larger problems by introducing a new distributed and parallel training architecture; (3) it demonstrates generalizability across different problem formulations by transferring knowledge within the same hypergraph; (4) it substantially boosts the solution accuracy compared with the prior art by suggesting a fine-tuning step using simulated annealing; and (5) it shows 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 a National Drug Code drug-substance hypergraph. Through extensive experimentation on various optimization problems, HypOp demonstrates superiority over existing unsupervised-learning-based solvers and generic optimization methods.

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