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Logic-Based Modeling

In: Handbook on Modelling for Discrete Optimization

Author

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  • John N Hooker

    (Carnegie Mellon University)

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.

Suggested Citation

  • John N Hooker, 2006. "Logic-Based Modeling," International Series in Operations Research & Management Science, in: Gautam Appa & Leonidas Pitsoulis & H. Paul Williams (ed.), Handbook on Modelling for Discrete Optimization, chapter 0, pages 61-102, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-32942-0_3
    DOI: 10.1007/0-387-32942-0_3
    as

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