GNN&GBDT-Guided Fast Optimizing Framework for Large-scale Integer Programming

Huigen Ye, Hua Xu, Hongyan Wang, Chengming Wang, Yu Jiang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:39864-39878, 2023.

Abstract

The latest two-stage optimization framework based on graph neural network (GNN) and large neighborhood search (LNS) is the most popular framework in solving large-scale integer programs (IPs). However, the framework can not effectively use the embedding spatial information in GNN and still highly relies on large-scale solvers in LNS, resulting in the scale of IP being limited by the ability of the current solver and performance bottlenecks. To handle these issues, this paper presents a GNN&GBDT-guided fast optimizing framework for large-scale IPs that only uses a small-scale optimizer to solve large-scale IPs efficiently. Specifically, the proposed framework can be divided into three stages: Multi-task GNN Embedding to generate the embedding space, GBDT Prediction to effectively use the embedding spatial information, and Neighborhood Optimization to solve large-scale problems fast using the small-scale optimizer. Extensive experiments show that the proposed framework can solve IPs with millions of scales and surpass SCIP and Gurobi in the specified wall-clock time using only a small-scale optimizer with 30% of the problem size. It also shows that the proposed framework can save 99% of running time in achieving the same solution quality as SCIP, which verifies the effectiveness and efficiency of the proposed framework in solving large-scale IPs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-ye23e, title = {{GNN}&{GBDT}-Guided Fast Optimizing Framework for Large-scale Integer Programming}, author = {Ye, Huigen and Xu, Hua and Wang, Hongyan and Wang, Chengming and Jiang, Yu}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {39864--39878}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/ye23e/ye23e.pdf}, url = {https://proceedings.mlr.press/v202/ye23e.html}, abstract = {The latest two-stage optimization framework based on graph neural network (GNN) and large neighborhood search (LNS) is the most popular framework in solving large-scale integer programs (IPs). However, the framework can not effectively use the embedding spatial information in GNN and still highly relies on large-scale solvers in LNS, resulting in the scale of IP being limited by the ability of the current solver and performance bottlenecks. To handle these issues, this paper presents a GNN&GBDT-guided fast optimizing framework for large-scale IPs that only uses a small-scale optimizer to solve large-scale IPs efficiently. Specifically, the proposed framework can be divided into three stages: Multi-task GNN Embedding to generate the embedding space, GBDT Prediction to effectively use the embedding spatial information, and Neighborhood Optimization to solve large-scale problems fast using the small-scale optimizer. Extensive experiments show that the proposed framework can solve IPs with millions of scales and surpass SCIP and Gurobi in the specified wall-clock time using only a small-scale optimizer with 30% of the problem size. It also shows that the proposed framework can save 99% of running time in achieving the same solution quality as SCIP, which verifies the effectiveness and efficiency of the proposed framework in solving large-scale IPs.} }
Endnote
%0 Conference Paper %T GNN&GBDT-Guided Fast Optimizing Framework for Large-scale Integer Programming %A Huigen Ye %A Hua Xu %A Hongyan Wang %A Chengming Wang %A Yu Jiang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-ye23e %I PMLR %P 39864--39878 %U https://proceedings.mlr.press/v202/ye23e.html %V 202 %X The latest two-stage optimization framework based on graph neural network (GNN) and large neighborhood search (LNS) is the most popular framework in solving large-scale integer programs (IPs). However, the framework can not effectively use the embedding spatial information in GNN and still highly relies on large-scale solvers in LNS, resulting in the scale of IP being limited by the ability of the current solver and performance bottlenecks. To handle these issues, this paper presents a GNN&GBDT-guided fast optimizing framework for large-scale IPs that only uses a small-scale optimizer to solve large-scale IPs efficiently. Specifically, the proposed framework can be divided into three stages: Multi-task GNN Embedding to generate the embedding space, GBDT Prediction to effectively use the embedding spatial information, and Neighborhood Optimization to solve large-scale problems fast using the small-scale optimizer. Extensive experiments show that the proposed framework can solve IPs with millions of scales and surpass SCIP and Gurobi in the specified wall-clock time using only a small-scale optimizer with 30% of the problem size. It also shows that the proposed framework can save 99% of running time in achieving the same solution quality as SCIP, which verifies the effectiveness and efficiency of the proposed framework in solving large-scale IPs.
APA
Ye, H., Xu, H., Wang, H., Wang, C. & Jiang, Y.. (2023). GNN&GBDT-Guided Fast Optimizing Framework for Large-scale Integer Programming. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:39864-39878 Available from https://proceedings.mlr.press/v202/ye23e.html.

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