Annals of Operations Research

, Volume 184, Issue 1, pp 295–314 | Cite as

Global propagation of side constraints for solving over-constrained problems



This article deals with the resolution of over-constrained problems using constraint programming, which often imposes to add to the constraint network new side constraints. These side constraints control how the initial constraints of the model should be satisfied or violated, to obtain solutions that have a practical interest. They are specific to each application. In our experiments, we show the superiority of a framework where side constraints are encoded by global constraints on new domain variables, which are directly included into the model. The case-study is a cumulative scheduling problem with over-loads. The objective is to minimize the total amount of over-loads. We augment the Cumulative global constraint of the constraint programming solver Choco with sweep and task interval violation-based algorithms. We provide a theoretical and experimental comparison of the two main approaches for encoding over-constrained problems with side constraints.


Constraint programming Over-constrained problems Cumulative scheduling 


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  1. Aggoun, A., & Beldiceanu, N. (1993). Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling, 17(7), 57–73. CrossRefGoogle Scholar
  2. Baptiste, P., Pape, C. L., & Peridy, L. (1998). Global constraints for partial CSPs: A case-study of resource and due date constraints. In Proc. CP (pp. 87–102). Google Scholar
  3. Baptiste, P., Le Pape, C., & Nuitjen, W. (1999). Satisfiability tests and time-bound adjustments for cumulative scheduling problems. Annals of Operations Research, 92, 305–333. CrossRefGoogle Scholar
  4. Beldiceanu, N., & Carlsson, M. (2002). A new multi-resource cumulatives constraint with negative heights. In Proc. CP (pp. 63–79). Google Scholar
  5. Benoist, T., Jeanjean, A., Rochart, G., Cambazard, H., Grellier, E., & Jussien, N. (2006). Subcontractors scheduling on residential buildings construction sites. ISS’06 Int. Sched. Symposium, Technical Report JSME-06-203 (pp. 32–37). Google Scholar
  6. Bistarelli, S., Montanari, U., Rossi, F., Schiex, T., Verfaillie, G., & Fargier, H. (1999). Semiring-based CSPs and valued CSPs: frameworks, properties, and comparison. Constraints, 4, 199–240. CrossRefGoogle Scholar
  7. Carlsson, M., Ottosson, G., & Carlson, B. (1997). An open-ended finite domain constraint solver. In Proc. PLILP (pp. 191–206). Google Scholar
  8. Caseau, Y., & Laburthe, F. (1996). Cumulative scheduling with task intervals. In Proc. JICSLP (Joint International Conference and Symposium on Logic Programming) (pp. 363–377). Google Scholar
  9. Choco, (2009). An open source Java CP library, documentation manual.
  10. Freuder, E. (1989). Partial constraint satisfaction. In Proc. IJCAI (pp. 278–283). Google Scholar
  11. Freuder, E., & Wallace, R. (1992). Partial constraint satisfaction. Artificial Intelligence, 58, 21–70. CrossRefGoogle Scholar
  12. Hoeve, W. J. V., Pesant, G., & Rousseau, L. M. (2006). On global warming: Flow-based soft global constraints. Journal of Heuristics, 12(4–5), 475–489. Google Scholar
  13. Lahrichi, A. (1982). The notions of Hump, Compulsory Part and their use in Cumulative Problems. C. R. Acad. Sci., 294, 209–211. Google Scholar
  14. Larrosa, J., & Dechter, R. (2003). Boosting search with variable elimination in constraint optimization and constraint satisfaction problems. Constraints, 8(3), 303–326. CrossRefGoogle Scholar
  15. Larrosa, J., & Meseguer, P. (1996). Exploiting the use of DAC in Max-CSP. In Proc. CP (pp. 308–322). Google Scholar
  16. Larrosa, J., & Schiex, T. (2004). Solving weighted csp by maintaining arc consistency. Artificial Intelligence, 159(1–2), 1–26. CrossRefGoogle Scholar
  17. Lopez, P., Erschler, J., & Esquirol, P. (1992). Ordonnancement de tâches sous contraintes : une approche énergétique. Automatique, Productique, Informatique Industrielle, 26(5–6), 453–481. Google Scholar
  18. Mercier, L., & Hentenryck, P. V. (2008). Edge finding for cumulative scheduling. INFORMS Journal on Computing, 20(1), 143–153. CrossRefGoogle Scholar
  19. Pesant, G. (2004). A regular language membership constraint for finite sequences of variables. In Proc. CP (pp. 482–495). Google Scholar
  20. Pesant, G., & Régin, J. C. (2005). Spread: A balancing constraint based on statistics. In Proc. CP (pp. 460–474). Google Scholar
  21. Petit, T. (2007). Propagation of practicability criteria. Research report 0701, Ecole des Mines de Nantes.
  22. Petit, T., & Poder, E. (2009). The soft cumulative constraint. Research report TR09/06/info, Ecole des Mines de Nantes. Google Scholar
  23. Petit, T., Régin, J. C., & Bessière, C. (2000). Meta constraints on violations for over constrained problems. In Proc. IEEE-ICTAI (pp. 358–365). Google Scholar
  24. Petit, T., Régin, J. C., & Bessière, C. (2001). Specific filtering algorithms for over constrained problems. In Proc. CP (pp. 451–463). Google Scholar
  25. Régin, J. C. (1996). Generalized arc consistency for global cardinality constraint. In Proc. AAAI (pp. 209–215). Google Scholar
  26. Régin, J. C. (2003). Using constraint programming to solve the maximum clique problem. In Proc. CP (pp. 634–648). Google Scholar
  27. Rudová, H., & Vlk, M. (2005). Multi-criteria soft constraints in timetabling. In Proc. MISTA (pp. 11–15). Google Scholar
  28. Schaus, P., Deville, Y., Dupont, P., & Régin, J. C. (2007). The deviation constraint. In Proc. CPAIOR (pp. 260–274). Google Scholar
  29. Stuckey, P. J. (Ed.) (2008). Principles and practice of constraint programming, 14th international conference, CP 2008, Sydney, Australia, September 14–18, 2008. Proceedings. Lecture Notes in Computer Science: Vol. 5202. Berlin: Springer. Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.École des Mines de NantesLINA UMR CNRS 6241Nantes Cedex 3France
  2. 2.CarquefouFrance

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