Title: Hypergraph Neural Network for Integer Programming with High-Degree Terms
Primary area: optimization
Keywords: Integer Programming, Nonlinear rogramming, Hypergraph Neural Network, Combinatorial Optimization, High-Degree Terms

Abstract: Complex real-world optimization problems often involve not only discrete decisions, but also nonlinear relationships between variables represented in constraints or objectives.
A class of such problems can be modeled as integer programming with high-degree terms, such as quadratic integer programming. The nonlinearity makes integer programming problems far more challenging than their linear counterparts. In this paper, we propose a hypergraph neural network (HNN) based method to solve integer programming with high-degree terms. First, we present a high-degree term-aware hypergraph representation to effectively capture both high-degree information and variable-constraint interdependencies. Then, a hypergraph neural network, that integrates convolution between variables and high-degree terms with convolution between variables and constraints, is proposed to predict solution values. Finally, a search process initialized from the predicted solutions is performed to further refine the results. Comprehensive experimental evaluations across a range of benchmarks demonstrate that our method consistently outperforms both learning-based approaches and state-of-the-art solvers, ultimately delivering superior solution quality with favorable efficiency.

TL;DR: This paper proposes a novel hypergraph neural network framework to solve integer programming problems with high-degree terms