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Horizontally Elastic Edge Finder Rule for Cumulative Constraint Based on Slack and Density

Authors Roger Kameugne , Sévérine Fetgo Betmbe , Thierry Noulamo , Clémentin Tayou Djamegni

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Author Details

Roger Kameugne
  • Faculty of Sciences, Department of Mathematics and Computer Science, University of Maroua, Cameroon
Sévérine Fetgo Betmbe
  • Faculty of Sciences, Department of Mathematics and Computer Science, University of Dschang, Cameroon
Thierry Noulamo
  • UIT Fotso Victor of Bandjoun, Department of Computer Engineering, University of Dschang, Cameroon
Clémentin Tayou Djamegni
  • Faculty of Sciences, Department of Mathematics and Computer Science, University of Dschang, Cameroon
  • UIT Fotso Victor of Bandjoun, Department of Computer Engineering, University of Dschang, Cameroon

Acknowledgements

The authors thank Dr. Dany Nantchouang and Prof. Emmanuel Hebrard for their proofreading.

Cite As Get BibTex

Roger Kameugne, Sévérine Fetgo Betmbe, Thierry Noulamo, and Clémentin Tayou Djamegni. Horizontally Elastic Edge Finder Rule for Cumulative Constraint Based on Slack and Density. In 29th International Conference on Principles and Practice of Constraint Programming (CP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 280, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CP.2023.20

Abstract

In this paper, we propose an enhancement of the filtering power of the edge finding rule, based on the Profile and the TimeTable data structures. The minimal slack and the maximum density criteria are used to select potential task intervals for the edge finding rule. The strong detection rule of the horizontally elastic edge finder of Fetgo and Tayou is then applied on those intervals, which results in a new filtering rule, named Slack-Density Horizontally Elastic Edge Finder. The new rule subsumes the edge finding rule and it is not comparable to the Gingras and Quimper horizontally elastic edge finder rule and the TimeTable edge finder rule. A two-phase filtering algorithm of complexity 𝒪(n²) (where n is the number of tasks sharing the resource) is proposed for the new rule. Improvements based on the TimeTable are obtained by considering fix part of external tasks which overlap with the potential task intervals. The detection and the adjustment of the improve algorithm are further increased, while the algorithm remains quadratic. Experimental results, on a well-known suite of benchmark instances of Resource-Constrained Project Scheduling Problems, show that the propounded algorithms are competitive with the state-of-the-art algorithms, in terms of running time and tree search reduction.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Planning and scheduling
  • Theory of computation → Constraint and logic programming
Keywords
  • Horizontally Elastic Scheduling
  • Edge Finder Rule
  • Profile
  • TimeTable
  • Resource-Constrained Project Scheduling Problem

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References

  1. Abderrahmane Aggoun and Nicolas Beldiceanu. Extending CHIP in order to Solve Complex Scheduling and Placement Problems. Mathl. Comput. Modelling, 17(7):57-73, 1993. URL: https://hal.archives-ouvertes.fr/hal-00442821.
  2. P. Baptiste, C.L. Pape, and W. Nuijten. Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems. International Series in Operations Research & Management Science. Springer US, 2012. URL: https://books.google.cm/books?id=qUzhBwAAQBAJ.
  3. Philippe Baptiste, Philippe Laborie, Claude Le Pape, and Wim Nuijten. Constraint-based scheduling and planning. In Handbook of Constraint Programming, volume 2 of Foundations of Artificial Intelligence, pages 761-799. Elsevier, 2006. Google Scholar
  4. Nicolas Beldiceanu and Mats Carlsson. A new multi-resource cumulatives constraint with negative heights. In CP, volume 2470 of Lecture Notes in Computer Science, pages 63-79. Springer, 2002. Google Scholar
  5. Frédéric Boussemart, Fred Hemery, Christophe Lecoutre, and Lakhdar Sais. Boosting systematic search by weighting constraints. In ECAI, pages 146-150. IOS Press, 2004. Google Scholar
  6. Rajkumar Buyya, M. Manzur Murshed, David Abramson, and Srikumar Venugopal. Scheduling parameter sweep applications on global grids: a deadline and budget constrained cost-time optimization algorithm. Softw. Pract. Exp., 35(5):491-512, 2005. Google Scholar
  7. Jacques Carlier, Eric Pinson, Abderrahim Sahli, and Antoine Jouglet. An O(n^2) algorithm for time-bound adjustments for the cumulative scheduling problem. Eur. J. Oper. Res., 286(2):468-476, 2020. Google Scholar
  8. Yves Caseau and François Laburthe. Improved CLP scheduling with task intervals. In ICLP, pages 369-383. MIT Press, 1994. Google Scholar
  9. Hamed Fahimi, Yanick Ouellet, and Claude-Guy Quimper. Linear-time filtering algorithms for the disjunctive constraint and a quadratic filtering algorithm for the cumulative not-first not-last. Constraints An Int. J., 23(3):272-293, 2018. Google Scholar
  10. Sévérine Fetgo Betmbe and Clémentin Tayou Djamegni. Horizontally Elastic Edge-Finder Algorithm for Cumulative Resource Constraint Revisited. In CARI 2020, THIES, Senegal, October 2020. URL: https://hal.archives-ouvertes.fr/hal-02931383.
  11. Sévérine Fetgo Betmbe and Clémentin Tayou Djamegni. Horizontally elastic edge-finder algorithm for cumulative resource constraint revisited. Oper. Res. Forum, 3(65), 2022. URL: https://doi.org/10.1007/s43069-022-00172-6.
  12. M. R. Garey and David S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, 1979. Google Scholar
  13. Steven Gay, Renaud Hartert, Christophe Lecoutre, and Pierre Schaus. Conflict ordering search for scheduling problems. In CP, volume 9255 of Lecture Notes in Computer Science, pages 140-148. Springer, 2015. Google Scholar
  14. Steven Gay, Renaud Hartert, and Pierre Schaus. Simple and scalable time-table filtering for the cumulative constraint. In CP, volume 9255 of Lecture Notes in Computer Science, pages 149-157. Springer, 2015. Google Scholar
  15. Vincent Gingras and Claude-Guy Quimper. Generalizing the edge-finder rule for the cumulative constraint. In IJCAI, pages 3103-3109. IJCAI/AAAI Press, 2016. Google Scholar
  16. Roger Kameugne, Sévérine Betmbe Fetgo, Vincent Gingras, Yanick Ouellet, and Claude-Guy Quimper. Horizontally elastic not-first/not-last filtering algorithm for cumulative resource constraint. In CPAIOR, volume 10848 of Lecture Notes in Computer Science, pages 316-332. Springer, 2018. Google Scholar
  17. Roger Kameugne and Laure Pauline Fotso. A cumulative not-first/not-last filtering algorithm in o(n2log(n)). Indian Journal of Pure and Applied Mathematics, 44:95-115, 2013. Google Scholar
  18. Roger Kameugne, Laure Pauline Fotso, and Joseph D. Scott. A quadratic extended edge-finding filtering algorithm for cumulative resource constraints. International Journal of Planning and Scheduling (IJPS), 1(4), 2013. Google Scholar
  19. Roger Kameugne, Laure Pauline Fotso, Joseph D. Scott, and Youcheu Ngo-Kateu. A quadratic edge-finding filtering algorithm for cumulative resource constraints. Constraints An Int. J., 19(3):243-269, 2014. Google Scholar
  20. Rainer Kolisch and Arno Sprecher. Psplib - a project scheduling problem library. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 96:205-216, 1996. Google Scholar
  21. Arnaud Letort, Nicolas Beldiceanu, and Mats Carlsson. A scalable sweep algorithm for the cumulative constraint. In CP, volume 7514 of Lecture Notes in Computer Science, pages 439-454. Springer, 2012. Google Scholar
  22. Luc Mercier and Pascal Van Hentenryck. Edge finding for cumulative scheduling. INFORMS J. Comput., 20(1):143-153, 2008. Google Scholar
  23. Pierre Ouellet and Claude-Guy Quimper. Time-table extended-edge-finding for the cumulative constraint. In CP, volume 8124 of Lecture Notes in Computer Science, pages 562-577. Springer, 2013. Google Scholar
  24. Yanick Ouellet and Claude-Guy Quimper. A o(n log ^2 n) checker and o(n^2 log n) filtering algorithm for the energetic reasoning. In CPAIOR, volume 10848 of Lecture Notes in Computer Science, pages 477-494. Springer, 2018. Google Scholar
  25. Charles Prud'homme, Jean-Guillaume Fages, and Xavier Lorca. Choco Solver Documentation. TASC, INRIA Rennes, LINA CNRS UMR 6241, COSLING S.A.S., 2016. URL: http://www.choco-solver.org.
  26. Andreas Schutt, Thibaut Feydy, and Peter J. Stuckey. Explaining time-table-edge-finding propagation for the cumulative resource constraint. In CPAIOR, volume 7874 of Lecture Notes in Computer Science, pages 234-250. Springer, 2013. Google Scholar
  27. Andreas Schutt and Armin Wolf. A new O(n^2logn) not-first/not-last pruning algorithm for cumulative resource constraints. In CP, volume 6308 of Lecture Notes in Computer Science, pages 445-459. Springer, 2010. Google Scholar
  28. Petr Vilím. Global Constraints in Scheduling. PhD thesis, Charles University in Prague, Faculty of Mathematics and Physics, Department of Theoretical Computer Science and Mathematical Logic, KTIML MFF, Universita Karlova, Malostranské náměstí 2/25, 118 00 Praha 1, Czech Republic, August 2007. URL: http://vilim.eu/petr/disertace.pdf.
  29. Petr Vilím. Edge finding filtering algorithm for discrete cumulative resources in o(kn log n). In CP'09: Proceedings of the 15th international conference on Principles and practice of constraint programming, pages 802-816, Berlin, Heidelberg, 2009. Springer-Verlag. URL: http://vilim.eu/petr/cp2009.pdf.
  30. Petr Vilím. Timetable edge finding filtering algorithm for discrete cumulative resources. In CPAIOR, volume 6697 of Lecture Notes in Computer Science, pages 230-245. Springer, 2011. Google Scholar
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