, Volume 20, Issue 3, pp 346–361

Lagrangian bounds from decision diagrams

  • David Bergman
  • Andre A. Cire
  • Willem-Jan van Hoeve

DOI: 10.1007/s10601-015-9193-y

Cite this article as:
Bergman, D., Cire, A.A. & van Hoeve, WJ. Constraints (2015) 20: 346. doi:10.1007/s10601-015-9193-y


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.


Decision diagrams Lagrangian relaxation Constraint propagation 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • David Bergman
    • 1
  • Andre A. Cire
    • 2
  • Willem-Jan van Hoeve
    • 3
  1. 1.School of Business, University of ConnecticutOne University PlaceStamfordUSA
  2. 2.Department of ManagementUniversity of Toronto ScarboroughTorontoCanada
  3. 3.Tepper School of Business, Carnegie Mellon UniversityPittsburghUSA

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