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Horizontally Elastic Edge-Finder Algorithm for Cumulative Resource Constraint Revisited

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Abstract

The success of constraint programming on scheduling problems comes from the low complexity and power of propagators. The data structure Profile recently introduced by Gingras and Quimper in Generalizing the edge-finder rule for the cumulative constraint. In: IJCAI, IJCAI/AAAI Press, pp 3103–3109, 2016, when applied to the edge-finder rule for the cumulative resource constraint (which we call horizontally elastic edge-finder) has improved the filtering power of this rule. In this paper, the algorithm proposed by Gingras and Quimper in Generalizing the edge-finder rule for the cumulative constraint. In: IJCAI, IJCAI/AAAI Press, pp 3103–3109, 2016 is revisited. It is proved that the data structure Profile can be further used for more adjustments. A new formulation of the horizontally elastic edge-finder rule is put forward. Similar to Gingras and Quimper in Generalizing the edge-finder rule for the cumulative constraint. In: IJCAI, IJCAI/AAAI Press, pp 3103–3109, 2016, an \(\mathcal {O}(kn^2)\) algorithm (where n is the number of tasks sharing the resource and \(k\le n\), the number of distinct capacities required by tasks) based on new attributes of the Profile data structure is proposed for the new rule. Experimental results on instances of Resource-Constrained Project Scheduling Problems (RCPSPs) from the benchmark suites highlight that using this new algorithm reduces the number of backtracks for the majority of instances with a slight increase in running time.

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Data Availability

The data sets analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors thank Vincent Gingras and Claude-Guy Quimper for their source code; Roger Kameugne and Claude-Guy Quimper for their advice; Lozzi Martial Meutem Kamtchueng, Dany Nantchouang and Jean-Pierre Lienou for their proofreading. The authors also thank the reviewers for their thoughtful comments and efforts toward improving our paper.

Funding

The first author is a member of the Doctoral College“Mathématiques, Informatiques, Biosciences et Géosciences de l’Environment” under the “Agence Universitaire de la Francophonie (AUF)”. She was partially funded by the “Agence Universitaire de la Francophonie (AUF)”.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Sévérine Fetgo Betmbe & Clémentin Tayou Djamegni

  2. IUT-FV de Bandjoun, University of Dschang, Dschang, Cameroon

    Clémentin Tayou Djamegni

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  1. Sévérine Fetgo Betmbe
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Correspondence to Sévérine Fetgo Betmbe.

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A preliminary version of this work was published in the proceedings of CARI 2020 [9].

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Fetgo Betmbe, S., Djamegni, C.T. Horizontally Elastic Edge-Finder Algorithm for Cumulative Resource Constraint Revisited. Oper. Res. Forum 3, 65 (2022). https://doi.org/10.1007/s43069-022-00172-6

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