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Strengthening Relaxed Decision Diagrams for Maximum Independent Set Problem: Novel Variable Ordering and Merge Heuristics

Authors Mohsen Nafar , Michael Römer

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Author Details

Mohsen Nafar
  • Bielefeld University, Germany
Michael Römer
  • Bielefeld University, Germany

Funding

This research was funded by the Return Programme of the Federal State of North Rhine Westphalia (NRW Rückkehrprogramm).

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Mohsen Nafar and Michael Römer. Strengthening Relaxed Decision Diagrams for Maximum Independent Set Problem: Novel Variable Ordering and Merge Heuristics. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CP.2024.21

Abstract

Finding high-quality bounds is key to devising efficient exact solution approaches for Discrete Optimization (DO) problems. To this end, Decision Diagrams (DDs) provide strong and generic bounding mechanisms. This paper focuses on so-called relaxed DDs which, by merging nodes, over-approximate the solution space of DO problems and provide dual bounds the quality of which hinges upon the ordering of the variables in the DD compilation and on the selection of the nodes to merge. Addressing the Maximum Independent Set Problem, we present a novel dynamic variable ordering strategy relying on induced subgraphs of the original graph, and a new tie-based merge heuristic. In a set of computational experiments, we show that our strategies yield much stronger bounds than the standard state-of-the-art approaches. Furthermore, implementing our heuristics in a DD-based branch-and-bound, we reduce the solution times by around 33 % on average and by more than 50 % on hard instances.

Subject Classification

ACM Subject Classification
  • Theory of computation → Discrete optimization
Keywords
  • Decision Diagram
  • Dynamic Programming
  • Maximum Independent Set Problem
  • Dual Bound

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References

  1. David Bergman, Andre A. Cire, Willem-Jan van Hoeve, and John Hooker. Decision Diagrams for Optimization. Springer Publishing Company, Incorporated, 1st edition, 2016. Google Scholar
  2. David Bergman, Andre A Cire, Willem-Jan van Hoeve, and John Hooker. Branch-and-bound based on decision diagrams. In Decision Diagrams for Optimization, pages 95-122. Springer, 2016. Google Scholar
  3. David Bergman, Andre A Cire, Willem-Jan Van Hoeve, and John N Hooker. Discrete optimization with decision diagrams. INFORMS Journal on Computing, 28(1):47-66, 2016. Google Scholar
  4. Quentin Cappart, David Bergman, Louis-Martin Rousseau, Isabeau Prémont-Schwarz, and Augustin Parjadis. Improving variable orderings of approximate decision diagrams using reinforcement learning. INFORMS Journal on Computing, 34(5):2552-2570, 2022. Google Scholar
  5. Quentin Cappart, Emmanuel Goutierre, David Bergman, and Louis-Martin Rousseau. Improving optimization bounds using machine learning: Decision diagrams meet deep reinforcement learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pages 1443-1451, 2019. Google Scholar
  6. Margarita P Castro, Andre A Cire, and J Christopher Beck. Decision diagrams for discrete optimization: A survey of recent advances. INFORMS Journal on Computing, 34(4):2271-2295, 2022. Google Scholar
  7. Mathijs de Weerdt, Robert Baart, and Lei He. Single-machine scheduling with release times, deadlines, setup times, and rejection. European Journal of Operational Research, 291(2):629-639, 2021. Google Scholar
  8. Nikolaus Frohner and Günther R Raidl. Merging quality estimation for binary decision diagrams with binary classifiers. In International Conference on Machine Learning, Optimization, and Data Science, pages 445-457. Springer, 2019. Google Scholar
  9. Nikolaus Frohner and Günther R Raidl. Towards improving merging heuristics for binary decision diagrams. In Learning and Intelligent Optimization: 13th International Conference, LION 13, Chania, Crete, Greece, May 27-31, 2019, Revised Selected Papers 13, pages 30-45. Springer, 2020. Google Scholar
  10. Xavier Gillard, Pierre Schaus, and Vianney Coppé. Ddo, a generic and efficient framework for mdd-based optimization. In Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence, pages 5243-5245, 2021. Google Scholar
  11. John N Hooker. Job sequencing bounds from decision diagrams. In International Conference on Principles and Practice of Constraint Programming, pages 565-578. Springer, 2017. Google Scholar
  12. Matthias Horn, Johannes Maschler, Günther R Raidl, and Elina Rönnberg. A*-based construction of decision diagrams for a prize-collecting scheduling problem. Computers & Operations Research, 126:105125, 2021. Google Scholar
  13. Mohsen Nafar and Michael Römer. Lookahead, merge and reduce for compiling relaxed decision diagrams for optimization. In International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research, pages 74-82. Springer, 2024. Google Scholar
  14. Mohsen Nafar and Michael Römer. Using clustering to strengthen decision diagram bounds for discrete optimization. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 8082-8089, 2024. Google Scholar
  15. Augustin Parjadis, Quentin Cappart, Louis-Martin Rousseau, and David Bergman. Improving branch-and-bound using decision diagrams and 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 446-455. Springer, 2021. Google Scholar
  16. Isaac Rudich, Quentin Cappart, and Louis-Martin Rousseau. Peel-and-bound: Generating stronger relaxed bounds with multivalued decision diagrams. In Christine Solnon, editor, 28th International Conference on Principles and Practice of Constraint Programming, CP 2022, July 31 to August 8, 2022, Haifa, Israel, volume 235 of LIPIcs, pages 35:1-35:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.CP.2022.35.
  17. Isaac Rudich, Quentin Cappart, and Louis-Martin Rousseau. Improved peel-and-bound: Methods for generating dual bounds with multivalued decision diagrams. Journal of Artificial Intelligence Research, 77:1489-1538, 2023. Google Scholar
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