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Job Sequencing Bounds from Decision Diagrams

  • Conference paper
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Principles and Practice of Constraint Programming (CP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

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Abstract

In recent research, decision diagrams have proved useful for the solution of discrete optimization problems. Their success relies on the use of relaxed decision diagrams to obtain bounds on the optimal value, either through a node merger or a node splitting mechanism. We investigate the potential of node merger to provide bounds for dynamic programming models that do not otherwise have a practical relaxation, in particular the job sequencing problem with time windows and state-dependent processing times. We prove general conditions under which a node merger operation yields a valid relaxation and apply them to job sequencing. Computational experiments show that, surprisingly, relaxed diagrams prove the optimal value when their size is only a small fraction of the size of an exact diagram. On the other hand, a relaxed diagram of fixed size ceases to provide a useful bound as the instances scale up.

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Notes

  1. 1.

    Problems with nonseparable objective functions can also be represented, as described in [21], but to simplify exposition we omit this possibility.

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Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    J. N. Hooker

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  1. J. N. Hooker
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Correspondence to J. N. Hooker .

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  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

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Hooker, J.N. (2017). Job Sequencing Bounds from Decision Diagrams. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_36

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  • DOI: https://doi.org/10.1007/978-3-319-66158-2_36

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  • Print ISBN: 978-3-319-66157-5

  • Online ISBN: 978-3-319-66158-2

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