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Efficient filtering for the Resource-Cost AllDifferent constraint

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Abstract

This paper studies a family of optimization problems where a set of items, each requiring a possibly different amount of resource, must be assigned to different slots for which the price of the resource can vary. The objective is then to assign items such that the overall resource cost is minimized. Such problems arise commonly in domains such as production scheduling in the presence of fluctuating renewable energy costs or variants of the Travelling Salesman Problem. In Constraint Programming, this can be naturally modeled in two ways: (a) with a sum of element constraints; (b) with a MinimumAssignment constraint. Unfortunately the sum of element constraints obtains a weak filtering and the MinimumAssignment constraint does not scale well on large instances. This work proposes a third approach by introducing the ResourceCostAllDifferent constraint and an associated incremental and scalable filtering algorithm, running in \(\mathcal {O}(n \cdot m)\), where n is the number of unbound variables and m is the maximum domain size of unbound variables. Its goal is to compute the total cost in a scalable manner by dealing with the fact that all assignments must be different. We first evaluate the efficiency of the new filtering on a real industrial problem and then on the Product Matrix Travelling Salesman Problem, a special case of the Asymmetric Travelling Salesman Problem. The study shows experimentally that our approach generally outperforms the decomposition and the MinimumAssignment ones for the problems we considered.

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Notes

  1. Although in practice the computation in a search tree is incremental.

  2. We also experimented with the version from [8] to get exact reduced costs, but it appeared to be very slow for the instances we considered, so we do not report any results regarding that implementation.

  3. According to preliminary experiments we conducted. We do not report any results when exact reduced costs are used.

  4. http://www.n-side.com/

  5. Accessible at http://performance-profile.info.ucl.ac.be/.

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Acknowledgements

This Research has been supported by the “Service Publique de Wallonie – Direction générale opérationnelle de l’Economie, de l’Emploi & de la Recherche” under the scope of the InduStore project.

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Authors and Affiliations

  1. Université Catholique de Louvain, Place Sainte Barbe 2 bte L5.02.01, 1348, Louvain-la-Neuve, Belgium

    Sascha Van Cauwelaert & Pierre Schaus

Authors
  1. Sascha Van Cauwelaert
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  2. Pierre Schaus
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Correspondence to Sascha Van Cauwelaert.

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This article belongs to the Topical Collection: Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming

Guest Editors: Michele Lombardi and Domenico Salvagnin

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Van Cauwelaert, S., Schaus, P. Efficient filtering for the Resource-Cost AllDifferent constraint. Constraints 22, 493–511 (2017). https://doi.org/10.1007/s10601-017-9269-y

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