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Handbook on Modelling for Discrete Optimization pp 61–102Cite as

Logic-Based Modeling

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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 88))

Abstract

Logic-based modeling can result in decision models that are more natural and easier to debug. The addition of logical constraints to mixed integer programming need not sacrifice computational speed and can even enhance it if the constraints are processed correctly. They should be written or automatically reformulated so as to be as nearly consistent or hyperarc consistent as possible. They should also be provided with a tight continuous relaxation. This chapter shows how to accomplish these goals for a number of logic-based constraints: formulas of propositional logic, cardinality formulas, 0–1 linear inequalities (viewed as logical formulas), cardinality rules, and mixed logical/linear constraints. It does the same for three global constraints that are popular in constraint programming systems: the all-different, element and cumulative constraints.

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Author information

Authors and Affiliations

  1. Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    John N Hooker

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  1. John N Hooker
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Editor information

Editors and Affiliations

  1. Operational Research Department, London School of Economics, UK

    Gautam Appa  & H. Paul Williams  & 

  2. Department of Mathematical and Physical Sciences, Aristotle University of Thessaloniki, Greece

    Leonidas Pitsoulis

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© 2006 Springer Science+Business Media, Inc.

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Hooker, J.N. (2006). Logic-Based Modeling. In: Appa, G., Pitsoulis, L., Williams, H.P. (eds) Handbook on Modelling for Discrete Optimization. International Series in Operations Research & Management Science, vol 88. Springer, Boston, MA. https://doi.org/10.1007/0-387-32942-0_3

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