A Graph-based Approach for Relating Integer Programs

Zachary Steever, Kyle Hunt, Mark Karwan, Junsong Yuan, Chase C. Murray (2024) A Graph-Based Approach for Relating Integer Programs. INFORMS Journal on Computing 0(0). https://doi.org/10.1287/ijoc.2023.0255

37 Pages Posted: 8 Mar 2021 Last revised: 2 Apr 2024

See all articles by Zachary Steever

Zachary Steever

University at Buffalo, Department of Industrial and Systems Engineering, Students

Kyle Hunt

University at Buffalo (SUNY) - School of Management

Mark Karwan

University at Buffalo

Junsong Yuan

University at Buffalo

Chase Murray

State University of New York (SUNY) - University at Buffalo

Date Written: March 25, 2024

Abstract

This paper presents a framework for classifying and comparing instances of integer linear programs (ILPs) based on their mathematical structure. It has long been observed that the structure of ILPs can play an important role in determining the effectiveness of certain solution techniques; those that work well for one class of ILPs are often found to be effective in solving similarly structured problems. In this work, the structure of a given ILP instance is captured via a graph-based representation, where decision variables and constraints are described by nodes, and edges denote the presence of decision variables in certain constraints. Using machine learning techniques for graph-structured data, we introduce two approaches for leveraging the graph representations for relating ILPs. In the first approach, a graph convolutional network (GCN) is employed to classify ILP graphs as having come from one of a known number of problem classes. The second approach makes use of latent features learned by the GCN to compare ILP graphs to one another directly. As part of the latter approach, we introduce a formal measure of graph-based structural similarity. A series of empirical studies indicate strong performance for both the classification and comparison procedures. Additional properties of ILP graphs – namely, losslessness and permutation invariance – are also explored via computational experiments.

Keywords: model structure; combinatorial optimization; mixed integer programming; neural network

Suggested Citation

Steever, Zachary and Hunt, Kyle and Karwan, Mark and Yuan, Junsong and Murray, Chase, A Graph-based Approach for Relating Integer Programs (March 25, 2024). Zachary Steever, Kyle Hunt, Mark Karwan, Junsong Yuan, Chase C. Murray (2024) A Graph-Based Approach for Relating Integer Programs. INFORMS Journal on Computing 0(0). https://doi.org/10.1287/ijoc.2023.0255, Available at SSRN: https://ssrn.com/abstract=3793042 or http://dx.doi.org/10.2139/ssrn.3793042

Zachary Steever

University at Buffalo, Department of Industrial and Systems Engineering, Students ( email )

NY
United States

Kyle Hunt (Contact Author)

University at Buffalo (SUNY) - School of Management ( email )

255 Jacobs Management Center
Buffalo, NY 14260
United States

Mark Karwan

University at Buffalo ( email )

12 Capen Hall
Buffalo, NY 14260
United States

Junsong Yuan

University at Buffalo ( email )

12 Capen Hall
Buffalo, NY 14260
United States

Chase Murray

State University of New York (SUNY) - University at Buffalo

Industrial & Systems Engineering
341 Bell Hall
Buffalo, NY 14260
United States

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