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

Sen Bai, Chunqi Yang, Xin Bai, Xin Zhang, Zhengang Jiang

TL;DR

A GPU-accelerated and continuous-annealing-enhanced training pipeline for BIPNN 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.

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.

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

TL;DR

A GPU-accelerated and continuous-annealing-enhanced training pipeline for BIPNN 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.

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.

Paper Structure

This paper contains 19 sections, 15 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Notations and Definitions
  3. BIPNN: HyperGNN-based Optimizer for PUBO-formulated BIP
  4. Modeling PUBO-formulated BIPs via Hypergraphs
  5. Neural Network-based Optimizer
  6. BIPNN: Polynomial & Unconstrained Reformulation of BIP
  7. Polynomial Reformulation of BIP
  8. Unconstrained Reformulation of BIP
  9. Discussion
  10. Experimental Results
  11. Comparison with Linearization-based BIP Solvers
  12. Comparison on Real-world Datasets
  13. Comparative Analysis on Hypergraph Generation Mechanism
  14. Ablation Study
  15. Conclusion
  16. ...and 4 more sections

Figures (15)

  • Figure 1: The BIPNN framework.
  • Figure 2: Modeling PUBO-formulated BIPs via hypergraphs.
  • Figure 3: To solve the hypergraph max-cut problem, BIPNN generates a new hypergraph structure. However, both of these hypergraphs can be utilized for training the HyperGNN model.
  • Figure 4: SCIP, $d=4$.
  • Figure 5: SCIP, $d=6$.
  • ...and 10 more figures