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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 36 / No. 9: AAAI-22 Technical Tracks 9

MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers

February 1, 2023

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Authors

Elias B. Khalil

Department of Mechanical & Industrial Engineering, University of Toronto Scale AI Research Chair in Data-Driven Algorithms for Modern Supply Chains


Christopher Morris

Mila - Quebec AI Institute and McGill University


Andrea Lodi

CERC, Polytechnique Montréal and Jacobs Technion-Cornell Institute, Cornell Tech and Technion - IIT


DOI:

10.1609/aaai.v36i9.21262


Abstract:

Mixed-integer programming (MIP) technology offers a generic way of formulating and solving combinatorial optimization problems. While generally reliable, state-of-the-art MIP solvers base many crucial decisions on hand-crafted heuristics, largely ignoring common patterns within a given instance distribution of the problem of interest. Here, we propose MIP-GNN, a general framework for enhancing such solvers with data-driven insights. By encoding the variable-constraint interactions of a given mixed-integer linear program (MILP) as a bipartite graph, we leverage state-of-the-art graph neural network architectures to predict variable biases, i.e., component-wise averages of (near) optimal solutions, indicating how likely a variable will be set to 0 or 1 in (near) optimal solutions of binary MILPs. In turn, the predicted biases stemming from a single, once-trained model are used to guide the solver, replacing heuristic components. We integrate MIP-GNN into a state-of-the-art MIP solver, applying it to tasks such as node selection and warm-starting, showing significant improvements compared to the default setting of the solver on two classes of challenging binary MILPs. Our code and appendix are publicly available at https://github.com/lyeskhalil/mipGNN.

Topics: AAAI

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HOW TO CITE:

Elias B. Khalil||Christopher Morris||Andrea Lodi MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers Proceedings of the AAAI Conference on Artificial Intelligence (2022) 10219-10227.

Elias B. Khalil||Christopher Morris||Andrea Lodi MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers AAAI 2022, 10219-10227.

Elias B. Khalil||Christopher Morris||Andrea Lodi (2022). MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers. Proceedings of the AAAI Conference on Artificial Intelligence, 10219-10227.

Elias B. Khalil||Christopher Morris||Andrea Lodi. MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers. Proceedings of the AAAI Conference on Artificial Intelligence 2022 p.10219-10227.

Elias B. Khalil||Christopher Morris||Andrea Lodi. 2022. MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers. "Proceedings of the AAAI Conference on Artificial Intelligence". 10219-10227.

Elias B. Khalil||Christopher Morris||Andrea Lodi. (2022) "MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers", Proceedings of the AAAI Conference on Artificial Intelligence, p.10219-10227

Elias B. Khalil||Christopher Morris||Andrea Lodi, "MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers", AAAI, p.10219-10227, 2022.

Elias B. Khalil||Christopher Morris||Andrea Lodi. "MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers". Proceedings of the AAAI Conference on Artificial Intelligence, 2022, p.10219-10227.

Elias B. Khalil||Christopher Morris||Andrea Lodi. "MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers". Proceedings of the AAAI Conference on Artificial Intelligence, (2022): 10219-10227.

Elias B. Khalil||Christopher Morris||Andrea Lodi. MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers. AAAI[Internet]. 2022[cited 2023]; 10219-10227.


ISSN: 2374-3468


Published by AAAI Press, Palo Alto, California USA
Copyright 2022, Association for the Advancement of
Artificial Intelligence 1900 Embarcadero Road, Suite
101, Palo Alto, California 94303 All Rights Reserved

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