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Air Traffic Controller Shift Scheduling by Reduction to CSP, SAT and SAT-Related Problems

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Principles and Practice of Constraint Programming (CP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8656))

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Abstract

In this paper we present our experience in solving Air Traffic Controller Shift Scheduling Problem. We give a formal definition of this optimization problem and introduce three encodings. The encodings make possible to formulate a very wide set of different scheduling requirements. The problem is solved by using SAT, MaxSAT, PB, SMT, CSP and ILP solvers. In combination with these solvers, three different optimization techniques are presented, a basic technique and its two modifications. The modifications use local search to modify some parts of the initial solution. Results indicate that SAT-related approaches outperform other solving methods used and that one of the introduced techniques which uses local search can significantly outperform the basic technique. We have successfully used these approaches to make shift schedules for one air traffic control center.

This work was partially supported by the Serbian Ministry of Science grant 174021.

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References

  1. Apt, K.R.: Principles of constraint programming. Cambridge University Press (2003)

    Google Scholar 

  2. Arnvig, M., Beermann, B., Köper, B., Maziul, M., Mellett, U., Niesing, C., Vogt, J.: Managing shiftwork in european atm. Literature Review. European Organisation for the Safety of Air Navigation (2006)

    Google Scholar 

  3. Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global constraint catalog. Technical report, SICS (2005)

    Google Scholar 

  4. Berre, D.L., Parrain, A.: The sat4j library, release 2.2. JSAT 7(2-3), 59–64 (2010)

    Google Scholar 

  5. Biere, A.: Lingeling, plingeling, picosat and precosat at sat race 2010. FMV Report Series Technical Report 10(1) (2010)

    Google Scholar 

  6. Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, February 2009. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  7. Burke, E.K., De Causmaecker, P., Berghe, G.V., Van Landeghem, H.: The state of the art of nurse rostering. J. Scheduling 7(6), 441–499 (2004)

    Article  MATH  Google Scholar 

  8. Chen, J.: A new sat encoding of the at-most-one constraint. In: Proceedings of the 9th International Workshop on Constraint Modelling and Reformulation (2010)

    Google Scholar 

  9. Chiarandini, M., Birattari, M., Socha, K., Rossi-Doria, O.: An effective hybrid algorithm for university course timetabling. J. Scheduling 9(5), 403–432 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cook, S.A.: The complexity of theorem-proving procedures. In: Harrison, M.A., Banerji, R.B., Ullman, J.D. (eds.) STOC, pp. 151–158. ACM (1971)

    Google Scholar 

  11. de Moura, L., Bjørner, N.S.: Z3: An efficient smt solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. Dutertre, B., De Moura, L.: The yices smt solver, vol. 2, p. 2 (2006), Tool paper at, http://yices.csl.sri.com/tool-paper.pdf

  13. Eén, N., Sörensson, N.: An extensible sat-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Eén, N., Sörensson, N.: Temporal induction by incremental sat solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)

    Article  Google Scholar 

  15. Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into sat. JSAT 2(1-4), 1–26 (2006)

    MATH  Google Scholar 

  16. EUROCONTROL. Shiftwork practices study - atm and related industries. DAP/SAF-2006/56 Brussels: EUROCONTROL (2006)

    Google Scholar 

  17. Committee for a Review of the En Route Air Traffic Control Complexity and Workload Model. Air traffic controller staffing in the en route domain: A review of the federal aviation administration’s task load model (2010)

    Google Scholar 

  18. Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: clasp: A Conflict-Driven Answer Set Solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 260–265. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Hebrard, E.: Mistral, a constraint satisfaction library. In: Proceedings of the 3rd International CSP Solver Competition, pp. 31–39

    Google Scholar 

  20. Klieber, W., Kwon, G.: Efficient cnf encoding for selecting 1 from n objects. In: Proc. International Workshop on Constraints in Formal Verification (2007)

    Google Scholar 

  21. Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: Qmaxsat: A partial max-sat solver. JSAT 8(1/2), 95–100 (2012)

    MathSciNet  Google Scholar 

  22. Marques-Silva, J.: The msuncore maxsat solver. In: SAT 2009 competitive events booklet: preliminary version, p. 151 (2009)

    Google Scholar 

  23. Merchez, S., Lecoutre, C., Boussemart, F.: Abscon: A prototype to solve csps with abstraction. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 730–744. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  24. Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.R.: Minizinc: Towards a standard cp modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  25. Roussel, O., Lecoutre, C.: Xml representation of constraint networks: Format xcsp 2.1. CoRR, abs/0902.2362 (2009)

    Google Scholar 

  26. Schulte, C., Lagerkvist, M., Tack, G.: Gecode (2006), Software download and online material at the website, http://www.gecode.org

  27. Sinz, C.: Towards an optimal cnf encoding of boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  28. Stojadinović, M., Marić, F.: mesat: Multiple encodings of csp to sat. Constraints (2014), doi:10.1007/s10601-014-9165-7

    Google Scholar 

  29. Tamura, N., Banbara, M.: Sugar: A csp to sat translator based on order encoding. In: Proceedings of the Third Constraint Solver Competition, pp. 65–69 (2008)

    Google Scholar 

  30. Tanjo, T., Tamura, N., Banbara, M.: Sugar++: a sat-based max-csp/cop solver. In: Proc. the Third International CSP Solver Competition, pp. 144–151 (2008)

    Google Scholar 

  31. EATCHIP Human Resources Team. Ats manpower planning in practice: Introduction to a qualitative and quantitative staffing methodology. HUM.ET1.ST02.2000-REP-01 Brussels: EUROCONTROL (1998)

    Google Scholar 

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Stojadinović, M. (2014). Air Traffic Controller Shift Scheduling by Reduction to CSP, SAT and SAT-Related Problems. In: O’Sullivan, B. (eds) Principles and Practice of Constraint Programming. CP 2014. Lecture Notes in Computer Science, vol 8656. Springer, Cham. https://doi.org/10.1007/978-3-319-10428-7_63

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  • DOI: https://doi.org/10.1007/978-3-319-10428-7_63

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10427-0

  • Online ISBN: 978-3-319-10428-7

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