An Efficient Translation Scheme for Representing Nurse Rostering Problems as Satisfiability Problems

Stefaan Haspeslagh, Tommy Messelis, Greet Vanden Berghe, Patrick De Causmaecker

Abstract

In this paper we present efficient translation schemes for converting nurse rostering problem instances into satisfiability problems (SAT). We define eight generic constraints types allowing the representation of a large number of nurse rostering constraints commonly found in literature. For each of the generic constraint types, we present efficient translation schemes to SAT. Special attention is paid to the representation of counting constraints. We developed a two way translation scheme for counting constraints using O(nlogn) variables and O(n2) clauses. We translated the instances of the First international nurse rostering competition 2010 to SAT and proved the infeasibility of the instances. The SAT translation was used for a hardness study of nurse rostering problem instances based on SAT features.

References

  1. Acharyya, S. (2008). A SAT Approach for Solving The Nurse Scheduling Problem. In IEEE Region 10 Conference.
  2. Argelich, J. and Manyà, F. (2006). Exact max-sat solvers for over-constrained problems. Journal of Heuristics, 12:375-392.
  3. Asín, R., Nieuwenhuis, R., Oliveras, A., and RodríguezCarbonell, E. (2009). Cardinality networks and their applications. In Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing, SAT 7809, pages 167-180.
  4. Bailleux, O. and Boufkhad, Y. (2003). Efficient CNF Encoding of Boolean Cardinality Constraints. In Rossi, F., editor, Principles and Practice of Constraint Programming - CP 2003, volume 2833 of Lecture Notes in Computer Science, pages 108-122. Springer Berlin / Heidelberg.
  5. Bilgin, B., De Causmaecker, P., Haspeslagh, S., Messelis, T., and Vanden Berghe, G. (2009). Hardness studies for nurse rostering problems. In LION, Trento, Italy, 14-18 January 2009.
  6. Burke, E. and Curtois, T. (2011). New computational results for nurse rostering benchmark instances. technical report, 2011. Technical report, School of Computer Science, University of Nottingham.
  7. Burke, E. K., Curtois, T., Post, G., Qu, R., and Veltman, B. (2008). A hybrid heuristic ordering and variable neighbourhood search for the nurse rostering problem. European Journal of Operational Research, 188(2):330 - 341.
  8. Burke, E. K., De Causmaecker, P., Petrovic, S., and Vanden Berghe, G. (2001). Fitness Evaluation for Nurse Scheduling Problems. In Proceedings of the Congress on Evolutionary Computation (CEC2001), pages 1139-1146.
  9. Cadoli, M. and Schaerf, a. (2005). Compiling problem specifications into SAT. Artificial Intelligence, 162(1- 2):89-120.
  10. Cook, S. A. (1971). The complexity of theorem-proving procedures. In Proceedings of the third annual ACM symposium on Theory of computing, STOC 7871, pages 151-158.
  11. Coˆ té, M.-C., Gendron, B., Quimper, C.-G., and Rousseau, L.-M. (2011). Formal languages for integer programming modeling of shift scheduling problems. Constraints, 16(1):54-76.
  12. Haspeslagh, S., DeCausmaecker, P., Schaerf, A., and Stlevik, M. (2012). The first international nurse rostering competition 2010. Annals of Operations Research, pages 1-16. 10.1007/s10479-012-1062-0.
  13. Leyton-Brown, K., Nudelman, E., and Shoham, Y. (2006). Learning the empirical hardness of optimization problems: The case of combinatorial auctions. In Van Hentenryck, P., editor, Principles and Practice of Constraint Programming - CP 2002, volume 2470 of Lecture Notes in Computer Science, pages 91-100. Springer Berlin / Heidelberg.
  14. Messelis, T., Haspeslagh, S., Vanden Berghe, G., and De Causmaecker, P. (2012). Hardness studies for nurse rostering problems using sat features. Technical report, CODeS, Department of Computer Science, KU Leuven KULAK.
  15. Nudelman, E., Leyton-Brown, K., Hoos, H., Devkar, A., and Shoham, Y. (2004). Understanding random sat: Beyond the clauses-to-variables ratio. In Wallace, M., editor, Principles and Practice of Constraint Programming - CP 2004, volume 3258 of Lecture Notes in Computer Science, pages 438-452. Springer Berlin / Heidelberg.
  16. Sinz, C. (2005). Towards an optimal cnf encoding of boolean cardinality constraints. In Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming (CP 2005), pages 827-831.
  17. Valouxis, C., Gogos, C., Goulas, G., Alefragis, P., and Housos, E. (2012). A systematic two phase approach for the nurse rostering problem. European Journal of Operational Research, 219(2):425 - 433.
  18. Xu, L., Hutter, F., Hoos, H. H., and Leyton-Brown, K. (2008). Satzilla: portfolio-based algorithm selection for sat. J. Artif. Int. Res., 32(1):565-606.
Download


Paper Citation


in Harvard Style

Haspeslagh S., Messelis T., Vanden Berghe G. and De Causmaecker P. (2013). An Efficient Translation Scheme for Representing Nurse Rostering Problems as Satisfiability Problems . In Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8565-39-6, pages 303-310. DOI: 10.5220/0004259103030310


in Bibtex Style

@conference{icaart13,
author={Stefaan Haspeslagh and Tommy Messelis and Greet Vanden Berghe and Patrick De Causmaecker},
title={An Efficient Translation Scheme for Representing Nurse Rostering Problems as Satisfiability Problems},
booktitle={Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2013},
pages={303-310},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004259103030310},
isbn={978-989-8565-39-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - An Efficient Translation Scheme for Representing Nurse Rostering Problems as Satisfiability Problems
SN - 978-989-8565-39-6
AU - Haspeslagh S.
AU - Messelis T.
AU - Vanden Berghe G.
AU - De Causmaecker P.
PY - 2013
SP - 303
EP - 310
DO - 10.5220/0004259103030310