  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.
