BIPNN: Learning to Solve Binary Integer Programming via Hypergraph Neural Networks

TL;DR

BIPNN introduces a novel hypergraph neural network framework that efficiently solves large-scale nonlinear binary integer programming problems by reformulating them into differentiable loss functions and employing GPU-accelerated training.

Contribution

This work presents the first unsupervised hypergraph neural network approach for nonlinear BIP, overcoming scalability issues of traditional solvers with a polynomial loss reformulation.

Findings

Outperforms existing methods on synthetic datasets.

Reduces training time significantly with GPU acceleration.

Generates high-quality solutions for real-world BIP problems.

Abstract

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems. Yet, they lack scalability for tackling nonlinear challenges. To handle nonlinearities, state-of-the-art Branch-and-Cut solvers employ linear relaxations, leading to exponential growth in auxiliary variables and severe computation limitations. To overcome these limitations, we propose BIPNN (Binary Integer Programming Neural Network), an unsupervised learning framework to solve nonlinear BIP problems via hypergraph neural networks (HyperGNN). Specifically, BIPNN reformulates BIPs-constrained, discrete, and nonlinear (sin, log, exp) optimization problems-into unconstrained, differentiable, and polynomial loss functions. The reformulation stems from the observation of a precise one-to-one mapping between polynomial BIP objectives and hypergraph structures, enabling the unsupervised training of HyperGNN to optimize BIP problems in an end-to-end manner. On this basis, we propose a GPU-accelerated and continuous-annealing-enhanced training pipeline for BIPNN. The pipeline enables BIPNN to optimize large-scale nonlinear terms in BIPs fully in parallel via straightforward gradient descent, thus significantly reducing the training cost while ensuring the generation of discrete, high-quality solutions. Extensive experiments on synthetic and real-world datasets highlight the superiority of our approach.