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Scalable addressing of high dimensional constrained combinatorialoptimization problems is a challenge that arises in several science andengineering disciplines. Recent work introduced novel application of graphneural networks for solving polynomial-cost unconstrained combinatorialoptimization problems. This paper proposes a new framework, called HypOp, whichgreatly advances the state of the art for solving combinatorial optimizationproblems in several aspects: (i) it generalizes the prior results toconstrained optimization problems with an arbitrary cost function; (ii) itbroadens the application to higher dimensional problems by leveraging ahypergraph neural network structure; (iii) it enables scalability to muchlarger problems by introducing a new distributed and parallel architecture forhypergraph neural network training; (iv) it demonstrates generalizability toother problem formulations by knowledge transfer from the learned experience ofaddressing one set of cost/constraints to another set for the same hypergraph;(v) it significantly boosts the solution accuracy compared with the prior artby suggesting a fine-tuning step using simulated annealing; (vi) HypOp shows aremarkable progress on benchmark examples, with run times improved by up tofivefold using a combination of fine-tuning and distributed trainingtechniques. The framework allows addressing a novel set of scientific problemsincluding hypergraph MaxCut problem, satisfiability problems (3SAT), andresource allocation. We showcase the application of HypOp in scientificdiscovery by solving a hypergraph MaxCut problem on the NDC drug-substancehypergraph. Through extensive experimentation on a variety of combinatorialoptimization problems, HypOp demonstrates superiority over existingunsupervised learning-based solvers and generic optimization methods.

HypOp: Distributed Constrained Combinatorial Optimization leveraging Hypergraph Neural Networks