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Duality in Optimization and Constraint Satisfaction

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Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3990))

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Abstract

We show that various duals that occur in optimization and constraint satisfaction can be classified as inference duals, relaxation duals, or both. We discuss linear programming, surrogate, Lagrangean, superadditive, and constraint duals, as well as duals defined by resolution and filtering algorithms. Inference duals give rise to nogood-based search methods and sensitivity analysis, while relaxation duals provide bounds. This analysis shows that duals may be more closely related than they appear, as are surrogate and Lagrangean duals. It also reveals common structure between solution methods, such as Benders decomposition and Davis-Putnam-Loveland methods with clause learning. It provides a framework for devising new duals and solution methods, such as generalizations of mini-bucket elimination.

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, USA

    J. N. Hooker

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  1. J. N. Hooker
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Editors and Affiliations

  1. Department of Computer Science, University of Toronto, Canada

    J. Christopher Beck

  2. School of Computing, University of Leeds, U.K.

    Barbara M. Smith

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© 2006 Springer-Verlag Berlin Heidelberg

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Hooker, J.N. (2006). Duality in Optimization and Constraint Satisfaction. In: Beck, J.C., Smith, B.M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2006. Lecture Notes in Computer Science, vol 3990. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11757375_3

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  • DOI: https://doi.org/10.1007/11757375_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34306-6

  • Online ISBN: 978-3-540-34307-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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