Document Open Access Logo

Solving LBBD Master Problems with Constraint Programming and Domain-Independent Dynamic Programming

Authors Jiachen Zhang , J. Christopher Beck

PDF
Thumbnail PDF

File

LIPIcs.CP.2024.32.pdf
  • Filesize: 1.67 MB
  • 21 pages

Document Identifiers

Author Details

Jiachen Zhang
  • Department of Mechanical and Industrial Engineering, University of Toronto, Canada
J. Christopher Beck
  • Department of Mechanical and Industrial Engineering, University of Toronto, Canada

Funding

  • Beck, J. Christopher: Natural Sciences and Engineering Research Council of Canada.

Cite As Get BibTex

Jiachen Zhang and J. Christopher Beck. Solving LBBD Master Problems with Constraint Programming and Domain-Independent Dynamic Programming. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CP.2024.32

Abstract

We investigate using Constraint Programming (CP) and Domain-Independent Dynamic Programming (DIDP) to solve the master problem in Logic-based Benders Decomposition (LBBD) models, in particular addressing the challenge of feasibility cut formulation. For CP, we exploit key variable manipulation, constraint-based expressions, and global constraints to construct three combinatorial cut encodings. For the state-based DIDP model, we propose two cut encoding approaches: using additional preconditions of state transitions or adding state constraints. Each of these approaches can be modeled using integer numeric variables or set variables, resulting in four novel encodings. We apply the three CP variants and four DIDP variants to simple assembly line balancing problems with sequence-dependent setup times type-1 (SUALBP-1). Experimental results show all approaches outperform a mixed-integer programming (MIP) based master problem and the state-of-the-art monolithic MIP model, with the three CP variants being superior to all of the DIDP approaches.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
Keywords
  • constraint programming
  • domain-independent dynamic programming
  • logic-based Benders decomposition
  • assembly line balancing
  • sequence-dependent setup

Metrics

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

References

  1. Sener Akpinar, Atabak Elmi, and Tolga Bektaş. Combinatorial benders cuts for assembly line balancing problems with setups. European Journal of Operational Research, 259(2):527-537, 2017. Google Scholar
  2. Carlos Andres, Cristobal Miralles, and Rafael Pastor. Balancing and scheduling tasks in assembly lines with sequence-dependent setup times. European Journal of Operational Research, 187(3):1212-1223, 2008. Google Scholar
  3. Jorge A Baier, Fahiem Bacchus, and Sheila A McIlraith. A heuristic search approach to planning with temporally extended preferences. Artificial Intelligence, 173(5-6):593-618, 2009. Google Scholar
  4. Ilker Baybars. A survey of exact algorithms for the simple assembly line balancing problem. Management science, 32(8):909-932, 1986. Google Scholar
  5. Christian Becker and Armin Scholl. A survey on problems and methods in generalized assembly line balancing. European journal of operational research, 168(3):694-715, 2006. Google Scholar
  6. Yossi Bukchin and Tal Raviv. Constraint programming for solving various assembly line balancing problems. Omega, 78:57-68, 2018. Google Scholar
  7. Yingyi Chu and Quanshi Xia. Generating benders cuts for a general class of integer programming problems. In Jean-Charles Régin and Michel Rueher, editors, Proceedings of the First International Conference on the Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2004), volume 3011, pages 127-136. Springer, Berlin Heidelberg, 2004. Google Scholar
  8. Maryam Daryalal, Hamed Pouya, and Marc Antoine DeSantis. Network migration problem: A hybrid logic-based benders decomposition approach. INFORMS Journal on Computing, 2023. Google Scholar
  9. Rasul Esmaeilbeigi, Bahman Naderi, and Parisa Charkhgard. New formulations for the setup assembly line balancing and scheduling problem. OR spectrum, 38:493-518, 2016. Google Scholar
  10. Michael Forbes, Mitchell Harris, Marijn Jansen, Femke van der Schoot, and Thomas Taimre. Combining optimisation and simulation using logic-based benders decomposition. arXiv preprint arXiv:2107.08390, 2021. Google Scholar
  11. Cheng Guo, Merve Bodur, Dionne M Aleman, and David R Urbach. Logic-based benders decomposition and binary decision diagram based approaches for stochastic distributed operating room scheduling. INFORMS Journal on Computing, 33(4):1551-1569, 2021. Google Scholar
  12. LLC Gurobi Optimization. Gurobi optimizer reference manual, 2021. Accessed on 2024-04-10. URL: http://www.gurobi.com.
  13. John Hooker. Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction. John Wiley & Sons, Inc., New York, 2000. Google Scholar
  14. John N Hooker. Planning and scheduling by logic-based benders decomposition. Operations research, 55(3):588-602, 2007. Google Scholar
  15. John N Hooker and Greger Ottosson. Logic-based benders decomposition. Mathematical Programming, 96(1):33-60, 2003. Google Scholar
  16. Chih-Wei Hsu, Benjamin W Wah, Ruoyun Huang, and Yixin Chen. Constraint partitioning for solving planning problems with trajectory constraints and goal preferences. In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI 2007), pages 1924-1929, 2007. Google Scholar
  17. IBM. IBM ILOG CPLEX Optimizer. Accessed on 2024-04-20. URL: https://www.ibm.com/products/ilog-cplex-optimization-studio/cplex-cp-optimizer.
  18. Naveen Kumar and Dalgobind Mahto. Assembly line balancing: a review of developments and trends in approach to industrial application. Global Journal of Researches in Engineering Industrial Engineering, 13(2):29-50, 2013. Google Scholar
  19. Ryo Kuroiwa and J. C. Beck. Domain-independent dynamic programming. arXiv preprint arXiv:2401.13883, 2024. Google Scholar
  20. Ryo Kuroiwa and J Christopher Beck. Domain-independent dynamic programming: Generic state space search for combinatorial optimization. In the 33rd International Conference on Automated Planning and Scheduling (ICAPS), 236–244., 2023. Google Scholar
  21. Ryo Kuroiwa and J Christopher Beck. Solving domain-independent dynamic programming problems with anytime heuristic search. In the 33rd International Conference on Automated Planning and Scheduling (ICAPS), 245–253., 2023. Google Scholar
  22. Florin Leutwiler and Francesco Corman. A logic-based benders decomposition for microscopic railway timetable planning. European Journal of Operational Research, 303(2):525-540, 2022. Google Scholar
  23. Marcus Ritt and Alysson M Costa. Improved integer programming models for simple assembly line balancing and related problems. International Transactions in Operational Research, 25(4):1345-1359, 2018. Google Scholar
  24. Francesca Rossi, Peter Van Beek, and Toby Walsh. Constraint programming. Foundations of Artificial Intelligence, 3:181-211, 2008. Google Scholar
  25. Armin Scholl, Nils Boysen, and Malte Fliedner. The assembly line balancing and scheduling problem with sequence-dependent setup times: problem extension, model formulation and efficient heuristics. OR spectrum, 35:291-320, 2013. Google Scholar
  26. Armin Scholl and Robert Klein. Salome: A bidirectional branch-and-bound procedure for assembly line balancing. INFORMS journal on Computing, 9(4):319-334, 1997. Google Scholar
  27. Paul Shaw. A constraint for bin packing. In International conference on principles and practice of constraint programming, pages 648-662. Springer, 2004. Google Scholar
  28. Tony T Tran, Arthur Araujo, and J Christopher Beck. Decomposition methods for the parallel machine scheduling problem with setups. INFORMS Journal on Computing, 28(1):83-95, 2016. Google Scholar
  29. Tony T Tran and J Christopher Beck. Logic-based benders decomposition for alternative resource scheduling with sequence dependent setups. In ECAI 2012, pages 774-779. IOS Press, 2012. Google Scholar
  30. Jiachen Zhang and J. C. Beck. Domain-independent dynamic programming and constraint programming approaches for assembly line balancing problems with setups. arXiv preprint arXiv:2403.06780, 2024. Google Scholar
  31. Hassan Zohali, Bahman Naderi, and Vahid Roshanaei. Solving the type-2 assembly line balancing with setups using logic-based benders decomposition. INFORMS Journal on Computing, 34(1):315-332, 2022. 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