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Global Constraints: A Survey

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Hybrid Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 45))

Abstract

Constraint programming (CP) is mainly based on filtering algorithms; their association with global constraints is one of the main strengths of CP because they exploit the specific structure of each constraint. This chapter is an overview ofthese two techniques. A collection of the most frequently used global constraints is given and some filtering algorithms are detailed. In addition, we try to identify how filtering algorithms can be designed. At last, we identify some problems that deserve to be addressed in the future.

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Notes

  1. 1.

    Van Hoeve and Régin gave an example of a scheduling alternative: consider a set of activities and suppose that each activity can be processed either on the factory line 1 formed by the set of unary resources R1, or on the factory line 2 formed by the set of unary resources R2. Thus, at the beginning, the set of resources that will be used by an activity is not known. Also the set of activities that will be processed by a resource is not known. However, it is useful to express that the activities that will be processed on each line must be pairwise different. This can be done by defining two alldiff constraints, involving the start variables of each activity, and by stating that a start variable will be involved in exactly one alldiff constraint. Van Hoeve and Régin shown how arc consistency can be efficiently establish for the conjunction of these 2 alldiff constraints.

  2. 2.

    This complexity comes from the integer capacities. In this case, the flow is augmented by at least one for each iteration.

  3. 3.

    This algorithm can be viewed as a generalization of the constructive disjunction in the case where several constraints must be satisfied and not only one.

  4. 4.

    Note that imposing an item means that the problem is equivalent to the problem where the item is ignored and K becomes K−w i and B becomes B−p i.

  5. 5.

    A partial function δ(q,x) does not have to be defined for any combination of q∈Q and x∈Σ; and if δ(q,x) is defined and equal to q′ then it does not exist another symbol y such that δ(q,y)=q′.

  6. 6.

    This is really at the same time because the two papers were presented during the same session at the same conference: CP’04.

  7. 7.

    Once again it was exactly at the same time, because the two papers were presented at the same conference : CP’06

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  1. I3S/CNRS, 2000, Université de Nice-Sophia Antipolis, route des Lucioles - Les Algorithmes - bt. Euclide B BP 121, 06903, Sophia Antipolis, Cedex, France

    Jean-Charles Régin

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  1. Jean-Charles Régin
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Correspondence to Jean-Charles Régin .

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  1. , Department of Computer Science, Brown University, Providence, 02912, Rhode Island, USA

    Pascal van Hentenryck

  2. , Department of Electronics, Computer Scie, Università di Bologna, Viale Risorgimento 2, Bologna, 40136, Italy

    Michela Milano

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Régin, JC. (2011). Global Constraints: A Survey. In: van Hentenryck, P., Milano, M. (eds) Hybrid Optimization. Springer Optimization and Its Applications, vol 45. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1644-0_3

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