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Lagrangian bounds from decision diagrams

Constraints volume 20, pages 346–361 (2015)Cite this article

Abstract

Relaxed decision diagrams have recently been used in constraint programming to improve constraint propagation and optimization reasoning. In most applications, however, a decision diagram is compiled with respect to a single combinatorial structure. We propose to expand this representation by incorporating additional constraints in the decision diagram via a Lagrangian relaxation. With this generic approach we can obtain stronger bounds from the same decision diagram, while the associated cost-based filtering allows for further refining the relaxation. Experimental results on the traveling salesman problem with time windows show that the improved Lagrangian bounds can drastically reduce solution times.

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Authors and Affiliations

  1. School of Business, University of Connecticut, One University Place, Stamford, CT, 06901, USA

    David Bergman

  2. Department of Management, University of Toronto Scarborough, 1265 Military Trail, Toronto, ON, M1C-1A4, Canada

    Andre A. Cire

  3. Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Willem-Jan van Hoeve

Authors
  1. David Bergman
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  2. Andre A. Cire
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  3. Willem-Jan van Hoeve
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Correspondence to Willem-Jan van Hoeve.

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Bergman, D., Cire, A.A. & van Hoeve, WJ. Lagrangian bounds from decision diagrams. Constraints 20, 346–361 (2015). https://doi.org/10.1007/s10601-015-9193-y

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  • DOI: https://doi.org/10.1007/s10601-015-9193-y

Keywords

  • Decision diagrams
  • Lagrangian relaxation
  • Constraint propagation