Distributed Constrained Combinatorial Optimization leveraging Hypergraph Neural Networks

Abstract

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.