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Optimization Bounds from Decision Diagrams in Haddock

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13884))

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Abstract

We study the automatic generation of primal and dual bounds from decision diagrams in constraint programming. In particular, we expand the functionality of the Haddock system to optimization problems by extending its specification language to include an objective function. We describe how restricted decision diagrams can be compiled in Haddock similar to the existing relaxed decision diagrams. Together, they provide primal and dual bounds on the objective function, which can be seamlessly integrated into the constraint programming search. The entire process is automatic and only requires a high-level user model specification. We evaluate our method on the sequential ordering problem and compare the performance of Haddock to a dedicated decision diagram approach. The results show that Haddock achieves comparable results in similar time, demonstrating the viability of our automated decision diagram procedures for constraint optimization problems.

Laurent Michel—Synchrony Chair in Cybersecurity.

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Notes

  1. 1.

    For a maximization, \(U^\downarrow (s_\top )\) and \(U^\uparrow (s_\bot )\) give the upper bound.

  2. 2.

    With a slight abuse of notation as we do not repeat the bounds on z and among since those properties are identical.

  3. 3.

    Source code located at https://github.com/IsaacRudich/PnB_SOP.

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Acknowledgements

Laurent Michel and Rebecca Gentzel were partially supported by Synchrony. Willem-Jan van Hoeve is partially supported by Office of Naval Research Grant No. N00014-21-1-2240 and National Science Foundation Award #1918102.

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Authors and Affiliations

  1. University of Connecticut, Storrs, CT, 06269, USA

    Rebecca Gentzel & Laurent Michel

  2. Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Willem-Jan van Hoeve

Authors
  1. Rebecca Gentzel
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  2. Laurent Michel
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  3. Willem-Jan van Hoeve
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Correspondence to Rebecca Gentzel .

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Editors and Affiliations

  1. Department of Management, University of Toronto Scarborough and Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Andre A. Cire

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Gentzel, R., Michel, L., van Hoeve, WJ. (2023). Optimization Bounds from Decision Diagrams in Haddock. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_11

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  • DOI: https://doi.org/10.1007/978-3-031-33271-5_11

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