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DOI: 10.4230/LIPIcs.CP.2024.32

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

Authors: Jiachen Zhang and J. Christopher Beck

Published in: LIPIcs, Volume 307, 30th International Conference on Principles and Practice of Constraint Programming (CP 2024)

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.

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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)

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@InProceedings{zhang_et_al:LIPIcs.CP.2024.32,
  author =	{Zhang, Jiachen and Beck, J. Christopher},
  title =	{{Solving LBBD Master Problems with Constraint Programming and Domain-Independent Dynamic Programming}},
  booktitle =	{30th International Conference on Principles and Practice of Constraint Programming (CP 2024)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-336-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{307},
  editor =	{Shaw, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2024.32},
  URN =		{urn:nbn:de:0030-drops-207171},
  doi =		{10.4230/LIPIcs.CP.2024.32},
  annote =	{Keywords: constraint programming, domain-independent dynamic programming, logic-based Benders decomposition, assembly line balancing, sequence-dependent setup}
}

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

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