Document Open Access Logo

Learning Precedences for Scheduling Problems with Graph Neural Networks

Authors Hélène Verhaeghe , Quentin Cappart , Gilles Pesant , Claude-Guy Quimper

PDF
Thumbnail PDF

File

LIPIcs.CP.2024.30.pdf
  • Filesize: 0.95 MB
  • 18 pages

Document Identifiers

Author Details

Hélène Verhaeghe
  • DTAI, KU Leuven, Belgium
Quentin Cappart
  • Polytechnique Montréal, Canada
Gilles Pesant
  • Polytechnique Montréal, Canada
Claude-Guy Quimper
  • Université Laval, Quebec, Canada

Funding

This research received funding from IVADO and the Canada First Research Excellence Fund / Apogée fund PostDoc-2022-2378128196 and in part by NSERC Discovery Grants 218028/2017. It also received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No 101070149, project Tuples.

Acknowledgements

We thank the anonymous reviewers for their constructive criticism which helped us improve the original version of the paper.

Cite As Get BibTex

Hélène Verhaeghe, Quentin Cappart, Gilles Pesant, and Claude-Guy Quimper. Learning Precedences for Scheduling Problems with Graph Neural Networks. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CP.2024.30

Abstract

The resource constrained project scheduling problem (RCPSP) consists of scheduling a finite set of resource-consuming tasks within a temporal horizon subject to resource capacities and precedence relations between pairs of tasks. It is NP-hard and many techniques have been introduced to improve the efficiency of CP solvers to solve it. The problem is naturally represented as a directed graph, commonly referred to as the precedence graph, by linking pairs of tasks subject to a precedence. In this paper, we propose to leverage the ability of graph neural networks to extract knowledge from precedence graphs. This is carried out by learning new precedences that can be used either to add new constraints or to design a dedicated variable-selection heuristic. Experiments carried out on RCPSP instances from PSPLIB show the potential of learning to predict precedences and how they can help speed up the search for solutions by a CP solver.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Artificial intelligence
  • Computing methodologies → Machine learning
  • Mathematics of computing → Combinatorial optimization
Keywords
  • Scheduling
  • Precedence graph
  • Graph neural network

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

References

  1. Jacek Blazewicz, Jan Karel Lenstra, and AHG Rinnooy Kan. Scheduling subject to resource constraints: classification and complexity. Discrete applied mathematics, 5(1):11-24, 1983. Google Scholar
  2. Lei Cai, Jundong Li, Jie Wang, and Shuiwang Ji. Line graph neural networks for link prediction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(9):5103-5113, 2021. Google Scholar
  3. Quentin Cappart, Didier Chételat, Elias B. Khalil, Andrea Lodi, Christopher Morris, and Petar Velickovic. Combinatorial optimization and reasoning with graph neural networks. Journal of Machine Learning Research, 24(130):1-61, 2023. Google Scholar
  4. Quentin Cappart, Thierry Moisan, Louis-Martin Rousseau, Isabeau Prémont-Schwarz, and Andre A Cire. Combining reinforcement learning and constraint programming for combinatorial optimization. In Proceedings of the AAAI Conference on Artificial Intelligence, 2021. Google Scholar
  5. Félix Chalumeau, Ilan Coulon, Quentin Cappart, and Louis-Martin Rousseau. Seapearl: A constraint programming solver guided by reinforcement learning. In Integration of Constraint Programming, Artificial Intelligence, and Operations Research: 18th International Conference, CPAIOR 2021, Vienna, Austria, July 5-8, 2021, Proceedings 18, pages 392-409. Springer, 2021. Google Scholar
  6. Mark Cheung. Geometric Deep Learning: Impact of Graph Structure on Graph Neural Networks. PhD thesis, Carnegie Mellon University, 2022. Google Scholar
  7. Geoffrey Chu and Peter J Stuckey. Learning value heuristics for constraint programming. In Integration of AI and OR Techniques in Constraint Programming: 12th International Conference, CPAIOR 2015, Barcelona, Spain, May 18-22, 2015, Proceedings 12, pages 108-123. Springer, 2015. Google Scholar
  8. Bert De Reyck et al. A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations. European Journal of Operational Research, 111(1):152-174, 1998. Google Scholar
  9. Emir Demirović, Geoffrey Chu, and Peter J Stuckey. Solution-based phase saving for cp: A value-selection heuristic to simulate local search behavior in complete solvers. In Principles and Practice of Constraint Programming: 24th International Conference, CP 2018, Lille, France, August 27-31, 2018, Proceedings 24, pages 99-108. Springer, 2018. Google Scholar
  10. Floris Doolaard and Neil Yorke-Smith. Online learning of variable ordering heuristics for constraint optimisation problems. Annals of Mathematics and Artificial Intelligence, pages 1-30, 2022. Google Scholar
  11. Federico Errica, Marco Podda, Davide Bacciu, and Alessio Micheli. A fair comparison of graph neural networks for graph classification. arXiv preprint arXiv:1912.09893, 2019. Google Scholar
  12. Maxime Gasse, Didier Chételat, Nicola Ferroni, Laurent Charlin, and Andrea Lodi. Exact combinatorial optimization with graph convolutional neural networks. Advances in neural information processing systems, 32, 2019. Google Scholar
  13. Xavier Glorot, Antoine Bordes, and Yoshua Bengio. Deep sparse rectifier neural networks. In Proceedings of the fourteenth international conference on artificial intelligence and statistics, pages 315-323. JMLR Workshop and Conference Proceedings, 2011. Google Scholar
  14. Carla Gomes and Meinolf Sellmann. Streamlined constraint reasoning. In International Conference on Principles and Practice of Constraint Programming, pages 274-289. Springer, 2004. Google Scholar
  15. Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. Advances in neural information processing systems, 30, 2017. Google Scholar
  16. Bo Han, Jiangchao Yao, Gang Niu, Mingyuan Zhou, Ivor Tsang, Ya Zhang, and Masashi Sugiyama. Masking: A new perspective of noisy supervision. Advances in neural information processing systems, 31, 2018. Google Scholar
  17. Elias Khalil, Hanjun Dai, Yuyu Zhang, Bistra Dilkina, and Le Song. Learning combinatorial optimization algorithms over graphs. Advances in neural information processing systems, 30, 2017. Google Scholar
  18. Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014. Google Scholar
  19. Rainer Kolisch and Arno Sprecher. Psplib-a project scheduling problem library: Or software-orsep operations research software exchange program. European journal of operational research, 96(1):205-216, 1997. Google Scholar
  20. Jan Karel Lenstra and AHG Rinnooy Kan. Complexity of scheduling under precedence constraints. Operations Research, 26(1):22-35, 1978. Google Scholar
  21. Yujia Li, Richard Zemel, Marc Brockschmidt, and Daniel Tarlow. Gated graph sequence neural networks. In International Conference on Learning Representations, 2016. Google Scholar
  22. Linyuan Lü and Tao Zhou. Link prediction in complex networks: A survey. Physica A: statistical mechanics and its applications, 390(6):1150-1170, 2011. Google Scholar
  23. Tom Marty, Tristan François, Pierre Tessier, Louis Gautier, Louis-Martin Rousseau, and Quentin Cappart. Learning a generic value-selection heuristic inside a constraint programming solver. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. Google Scholar
  24. Matthew W Moskewicz, Conor F Madigan, Ying Zhao, Lintao Zhang, and Sharad Malik. Chaff: Engineering an efficient sat solver. In Proceedings of the 38th annual Design Automation Conference, pages 530-535, 2001. Google Scholar
  25. Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high-performance deep learning library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. dquotesingle Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems 32, pages 8024-8035. Curran Associates, Inc., 2019. URL: http://papers.neurips.cc/paper/9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf.
  26. A Alan B Pritsker, Lawrence J Waiters, and Philip M Wolfe. Multiproject scheduling with limited resources: A zero-one programming approach. Management science, 16(1):93-108, 1969. Google Scholar
  27. Patrick Prosser. The dynamics of dynamic variable ordering heuristics. In Principles and Practice of Constraint Programming—CP98: 4th International Conference, CP98 Pisa, Italy, October 26-30, 1998 Proceedings 4, pages 17-23. Springer, 1998. Google Scholar
  28. Franco Scarselli, Marco Gori, Ah Chung Tsoi, Markus Hagenbuchner, and Gabriele Monfardini. The graph neural network model. IEEE transactions on neural networks, 20(1):61-80, 2008. Google Scholar
  29. Andreas Schutt, Thibaut Feydy, and Peter J Stuckey. Explaining time-table-edge-finding propagation for the cumulative resource constraint. In Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems: 10th International Conference, CPAIOR 2013, Yorktown Heights, NY, USA, May 18-22, 2013. Proceedings 10, pages 234-250. Springer, 2013. Google Scholar
  30. Wen Song, Zhiguang Cao, Jie Zhang, Chi Xu, and Andrew Lim. Learning variable ordering heuristics for solving constraint satisfaction problems. Engineering Applications of Artificial Intelligence, 109:104603, 2022. Google Scholar
  31. Florent Teichteil-Königsbuch, Guillaume Povéda, Guillermo González de Garibay Barba, Tim Luchterhand, and Sylvie Thiébaux. Fast and robust resource-constrained scheduling with graph neural networks. In Sven Koenig, Roni Stern, and Mauro Vallati, editors, Proceedings of the Thirty-Third International Conference on Automated Planning and Scheduling, July 8-13, 2023, Prague, Czech Republic, pages 623-633. AAAI Press, 2023. URL: https://doi.org/10.1609/ICAPS.V33I1.27244.
  32. Ronald van Driel, Emir Demirović, and Neil Yorke-Smith. Learning variable activity initialisation for lazy clause generation solvers. In Integration of Constraint Programming, Artificial Intelligence, and Operations Research: 18th International Conference, CPAIOR 2021, Vienna, Austria, July 5-8, 2021, Proceedings 18, pages 62-71. Springer, 2021. Google Scholar
  33. Mathieu Vavrille, Charlotte Truchet, and Charles Prud’homme. Solution sampling with random table constraints. Constraints, pages 1-33, 2022. Google Scholar
  34. Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio. Graph attention networks. In International Conference on Learning Representations, 2018. Google Scholar
  35. Petr Vilím. Timetable edge finding filtering algorithm for discrete cumulative resources. In Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems: 8th International Conference, CPAIOR 2011, Berlin, Germany, May 23-27, 2011. Proceedings 8, pages 230-245. Springer, 2011. Google Scholar
  36. Julien Vion and Sylvain Piechowiak. Une simple heuristique pour rapprocher dfs et lns pour les cop. Proceedings of JFPC’17, pages 39-45, 2017. Google Scholar
  37. Minjie Wang, Da Zheng, Zihao Ye, Quan Gan, Mufei Li, Xiang Song, Jinjing Zhou, Chao Ma, Lingfan Yu, Yu Gai, Tianjun Xiao, Tong He, George Karypis, Jinyang Li, and Zheng Zhang. Deep graph library: A graph-centric, highly-performant package for graph neural networks. arXiv preprint arXiv:1909.01315, 2019. Google Scholar
  38. Lingfei Wu, Peng Cui, Jian Pei, Liang Zhao, and Le Song. Graph neural networks. Springer, 2022. Google Scholar
  39. Muhan Zhang and Yixin Chen. Link prediction based on graph neural networks. Advances in neural information processing systems, 31, 2018. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact