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Managing dynamic CSPs with preferences

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Abstract

We present a new framework, managing Constraint Satisfaction Problems (CSPs) with preferences in a dynamic environment. Unlike the existing CSP models managing one form of preferences, ours supports four types, namely: unary and binary constraint preferences, composite preferences and conditional preferences. This offers more expressive power in representing a wide variety of dynamic constraint applications under preferences and where the possible changes are known and available a priori. Conditional preferences allow some preference functions to be added dynamically to the problem, during the resolution process, if a given condition on some variables is true. A composite preference is a higher level of preference among the choices of a composite variable. Composite variables are variables whose possible values are CSP variables. In other words, this allows us to represent disjunctive CSP variables. The preferences are viewed as a set of soft constraints using the fuzzy CSP framework. Solving constraint problems with preferences consists in finding a solution satisfying all the constraints while optimizing the global preference value. This is handled by four variants of the branch and bound algorithm, we propose in this paper, and where constraint propagation is used to improve the time efficiency in practice. In order to evaluate and compare the performance of these four strategies, we conducted an experimental study on randomly generated dynamic CSPs with quantitative preferences. The results are reported and discussed in the paper.

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Notes

  1. There are special cases where CSPs are solved in polynomial time, for instance, the case where a CSP network is a tree [15, 19].

  2. We call CSP variables, the variables of a traditional CSP.

  3. In this paper, we are assuming that the constraints are binary and are defined in extension. For instance, the constraint C ij between 2 variables X i and X j is the subset of the Cartesian product of X i ’s and X j ’s domains.

  4. Note that we only consider here the case of binary constraints. Non binary constraints can actually be converted into binary ones in polynomial time as shown in [2].

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  1. University of Regina, Regina, Saskatchewan, Canada

    Malek Mouhoub & Amrudee Sukpan

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  1. Malek Mouhoub
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  2. Amrudee Sukpan
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Correspondence to Malek Mouhoub.

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Mouhoub, M., Sukpan, A. Managing dynamic CSPs with preferences. Appl Intell 37, 446–462 (2012). https://doi.org/10.1007/s10489-012-0338-z

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